Acceleration and motion graphs

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수업 노트

Big idea: acceleration and motion graphs

Key concept: Relationships. Acceleration is change in velocity divided by time. The gradient of a velocity-time graph gives acceleration and the area beneath it gives displacement.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Motion models help analyse transport and stopping distances.

Speed & Velocity

Speed = distance travelled per unit time; a scalar quantity (magnitude only).
Equation: v = \frac{s}{t}, where v in m/s, s in m, t in s.
Average speed = total distance / total time; useful when speed varies.
Velocity = speed in a given direction; a vector quantity (magnitude and direction).
Velocity uses displacement (vector) instead of distance.
Same speed but different directions → different velocities.

A person walking at 2.0 m/s and a bee flying at 4.5 m/s, illustrating speed.

Acceleration

Acceleration = rate of change of velocity; a = \frac{\Delta v}{\Delta t}, units m/s².
Change in velocity: \Delta v = v - u (final minus initial).
Positive acceleration = speeding up; negative acceleration (deceleration) = slowing down.
Any change in velocity (speed up, slow down, change direction) is acceleration.
Formula triangle: cover the quantity to find; a = \frac{\Delta v}{\Delta t}, \Delta v = a \times \Delta t, \Delta t = \frac{\Delta v}{a}.

Examples of positive and negative acceleration

Distance-Time Graphs

Distance-time graph: straight line = constant speed; horizontal line = stationary.
Gradient = speed; steeper slope = faster speed.
Curved line = changing speed (acceleration/deceleration); increasing gradient = speeding up, decreasing = slowing down.
To calculate speed: draw a large gradient triangle, find \frac{\Delta y}{\Delta x}.
Always check units (e.g., km → m, min → s).

The gradient of a distance-time graph, found from the change in distance (Δy) over the change in time (Δx), gives the speed.

Speed-Time Graphs

Speed-time graph: straight line = constant acceleration; horizontal line = constant speed (zero acceleration).
Gradient = acceleration; positive gradient = acceleration, negative = deceleration.
Area under graph = distance travelled.
Split area into triangles and rectangles: triangle area = \frac{1}{2}bh, rectangle area = bh.
Total distance = sum of all areas under the line.

Calculating Acceleration from Speed-Time Graphs

For constant acceleration: gradient = \frac{\Delta v}{\Delta t} using a straight line.
For changing acceleration: draw a tangent at the point; gradient of tangent = instantaneous acceleration.
A tangent is a straight line that just touches the curve at that point.
Use a large gradient triangle on the tangent to calculate \frac{\Delta y}{\Delta x}.

Freefall

In absence of air resistance, all objects fall with same acceleration: g = 9.8 \, \text{m/s}² (acceleration of freefall).
Weight W = mg, where g is gravitational field strength (N/kg).
With air resistance: forces are weight (down) and air resistance (up).
Air resistance increases with speed; when it equals weight, resultant force = 0 → terminal velocity.
Skydiver: initially accelerates, then air resistance increases, eventually reaches terminal velocity; deploying parachute increases air resistance → deceleration to a lower terminal velocity.
In a vacuum (no air resistance), objects never reach terminal velocity; they accelerate at g continuously.

Think like a scientist

Measure a toy trolley's speed at different times as it moves down a low ramp.
Comparison: the elapsed time after release. Outcome: the trolley's speed in metres per second.
Control: use the same ramp angle and release point. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Motion models help analyse transport and stopping distances.
A straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

슬라이드

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연습 문제

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1.Which of the following is a scalar quantity?
Easy
- Avelocity
- Bdisplacement
- Cacceleration
- Dspeed
2.What is the acceleration of free fall near Earth's surface?
Easy
- A9.8 m/s
- B9.8 m/s²
- C9.8 m/s² downward
- D9.8 N/kg
3.On a distance-time graph, a horizontal line indicates that the object is:
Easy
- Aaccelerating
- Bmoving at constant speed
- Cstationary
- Ddecelerating
4.Which of the following is the correct definition of velocity?
Easy
- ADistance travelled per unit time
- BSpeed in a given direction
- CChange in displacement per unit time
- DRate of change of speed
5.The area under a speed-time graph represents:
Easy
- Aacceleration
- Bvelocity
- Cdistance travelled
- Ddeceleration
6.An object accelerates from 4 m/s to 10 m/s in 3 s. What is its acceleration?
Medium
- A2 m/s²
- B3 m/s²
- C4 m/s²
- D6 m/s²
7.On a speed-time graph, a straight line with negative gradient represents:
Easy
- Aconstant acceleration
- Bconstant deceleration
- Cconstant speed
- Dincreasing acceleration
8.A skydiver falls from a plane. After reaching terminal velocity, the parachute opens. Which statement is correct?
Medium
- AThe skydiver immediately stops falling.
- BThe skydiver accelerates upward.
- CThe skydiver decelerates to a lower terminal velocity.
- DThe skydiver continues at the same terminal velocity.

더 많은 문제

9.A car travels at 20 m/s for 5 s, then at 30 m/s for 10 s. What is the total distance travelled?
Medium
- A100 m
- B300 m
- C400 m
- D500 m
10.A cyclist travels 360 m in 60 s. What is the average speed in m/s?
Easy
- A6 m/s
- B60 m/s
- C0.17 m/s
- D10 m/s
11.A car travels along a straight road. The speed-time graph for the car's journey is a straight line from (0 s, 0 m/s) to (10 s, 20 m/s). What is the acceleration of the car?
Medium
- A2 m/s²
- B0.5 m/s²
- C20 m/s²
- D10 m/s²
12.The speed-time graph of a skydiver shows a curve that becomes horizontal. What does the horizontal section represent?
Medium
- AThe skydiver is accelerating
- BThe skydiver is stationary
- CThe skydiver is moving at terminal velocity
- DThe skydiver is decelerating
13.A train travels 120 m in 54 s. What is its average speed?
Easy
- A2.22 m/s
- B0.45 m/s
- C6.48 m/s
- D6480 m/s
14.The speed-time graph of a car consists of a triangle from 0 to 10 s (speed increasing from 0 to 20 m/s) followed by a rectangle from 10 to 30 s (constant speed 20 m/s). What is the total distance travelled?
Medium
- A500 m
- B400 m
- C600 m
- D300 m
15.An object is moving at constant speed in a circle. Which statement about its velocity is correct?
Medium
- AVelocity is constant because speed is constant
- BVelocity changes because direction changes
- CVelocity is zero
- DVelocity is equal to speed
16.Which quantity is a vector?
Easy
- ASpeed
- BDistance
- CVelocity
- DTime
17.A skydiver jumps from a plane. Which statement about the forces acting on the skydiver is correct when terminal velocity is reached?
Medium
- AWeight is greater than air resistance
- BAir resistance is greater than weight
- CWeight equals air resistance
- DThere are no forces acting on the skydiver
18.A car decelerates from 30 m/s to 10 m/s in 5 s. What is the deceleration?
Medium
- A4 m/s²
- B8 m/s²
- C-4 m/s²
- D-8 m/s²
19.The distance-time graph for a cyclist is a straight line sloping upward. What does this indicate?
Easy
- AThe cyclist is stationary
- BThe cyclist is moving at constant speed
- CThe cyclist is accelerating
- DThe cyclist is decelerating
20.A student measures the time taken for a ball to fall from a height of 2.0 m using a stopwatch. The student repeats the measurement five times and obtains the following readings: 0.64 s, 0.66 s, 0.63 s, 0.65 s, 0.67 s. What is the most likely value for the time of fall?
Medium
- A0.65 s
- B0.64 s
- C0.66 s
- D0.63 s
21.A student investigates the motion of a trolley rolling down a ramp. She measures the distance travelled by the trolley every 0.2 s using a ticker-tape timer. The tape shows dots that are initially close together and then gradually become further apart. What does this pattern indicate about the motion of the trolley?
Easy
- AThe trolley is accelerating.
- BThe trolley is moving at constant speed.
- CThe trolley is decelerating.
- DThe trolley is stationary.
22.In an experiment to determine the acceleration of free fall, a student drops a steel ball from a height of 1.5 m and measures the time of fall using a light gate. The measured time is 0.55 s. Which of the following is the most likely reason for the discrepancy between the measured acceleration (calculated from s = ½at²) and the accepted value of 9.8 m/s²?
Medium
- AAir resistance acting on the ball.
- BThe height was measured incorrectly.
- CThe ball was not dropped exactly from rest.
- DThe light gate timing was triggered late.
23.A student uses a stopwatch to measure the time for 20 oscillations of a pendulum. She records 30.4 s. What is the time for one oscillation?
Easy
- A1.52 s
- B30.4 s
- C0.66 s
24.A car travels at a constant speed of 20 m/s for 10 s. It then decelerates uniformly at 2 m/s² until it stops. What is the total distance travelled by the car?
Medium
- A300 m
- B200 m
- C100 m
- D400 m
25.A skydiver jumps from a plane. Which of the following speed-time graphs best represents her motion from the moment she jumps until just before she opens her parachute?
Medium
- AA curve that starts with a steep positive gradient, then gradually becomes less steep and finally horizontal.
- BA straight line with constant positive gradient.
- CA curve that starts with a shallow positive gradient, then becomes steeper and finally horizontal.
- DA straight line with constant negative gradient.
26.A student measures the speed of a moving trolley using two light gates connected to a datalogger. The trolley passes the first gate at time 0.00 s and the second gate at time 0.25 s. The distance between the gates is 0.50 m. What is the average speed of the trolley between the gates?
Easy
- A2.0 m/s
- B0.125 m/s
- C0.50 m/s
- D4.0 m/s
27.A student plots a speed-time graph for a moving object. To find the acceleration at a particular instant, she draws a tangent to the curve at that point and calculates its gradient. Which of the following is the correct reason for drawing a tangent?
Medium
- AThe gradient of the tangent gives the instantaneous acceleration.
- BThe area under the tangent gives the distance travelled.
- CThe gradient of the tangent gives the average acceleration.
- DThe tangent shows the direction of motion.
28.Which of the following is a vector quantity?
Easy
- AVelocity
- BSpeed
- CDistance
- DTime
29.What is the definition of speed?
Easy
- ADistance travelled per unit time
- BChange in velocity per unit time
- CSpeed in a given direction
- DRate of change of displacement
30.What does a horizontal line on a distance-time graph indicate?
Easy
- AThe object is accelerating
- BThe object is moving at constant speed
- CThe object is stationary
- DThe object is decelerating
31.Complete the sentence:
Easy
The acceleration of free fall near the Earth's surface is approximately ____ m/s².
32.A car travels 150 m in 10 s. What is its average speed in m/s?
Easy
33.A car accelerates uniformly from rest at 2 m/s² for 5 seconds. What is its final velocity?
Medium
34.A car accelerates uniformly from rest to 20 m/s in 8 seconds. What is its acceleration?
Medium
35.An object accelerates uniformly from rest at 2 m/s² for 5 seconds. What is its final velocity?
Easy
- A10 m/s
- B2.5 m/s
- C0.4 m/s
- D20 m/s
36.Which of the following is true for an object falling in a vacuum near Earth's surface?
Easy
- AIt accelerates at 9.8 m/s² regardless of mass
- BIt falls at constant speed
- CHeavier objects fall faster
- DIt decelerates due to air resistance
37.The gradient of a distance-time graph represents acceleration.
Easy
True or false?
38.Which of the following are vector quantities? (Select all that apply.)
Medium
- Avelocity
- Bspeed
- Cacceleration
- Ddistance
- Edisplacement
39.Match each quantity to its correct description.
Easy
- speed
- velocity
- acceleration
- rate of change of velocity
- distance travelled per unit time
- speed in a given direction
40.Arrange the following stages of a skydiver's fall in the correct order from the moment they jump until just before opening the parachute.
Medium
- accelerates downward
- reaches terminal velocity
- air resistance increases
- forces become balanced
41.Measure a toy trolley's speed at different times as it moves down a low ramp. What is the independent variable?
Easy
- Athe elapsed time after release
- Bthe trolley's speed in metres per second
- Cthe number of repeated trials
- Dthe scientific explanation written afterwards
42.Measure a toy trolley's speed at different times as it moves down a low ramp. Which observation or quantity is the dependent variable?
Easy
- Athe elapsed time after release
- Bthe trolley's speed in metres per second
- Cthe title given to the investigation
- Dthe number of references in the report
43.Measure a toy trolley's speed at different times as it moves down a low ramp. Which decision best controls another factor in this comparison?
Medium
- Achange every condition for each trial
- Buse a different measurement method for every result
- Cuse the same ramp angle and release point
- Drecord only results that agree with the prediction
44.Measure a toy trolley's speed at different times as it moves down a low ramp. Why should the class repeat measurements or check multiple comparable observations?
Medium
- ATo guarantee that every systematic error disappears
- BTo make an unsupported prediction become correct
- CTo avoid reporting results that disagree with a model
- DTo assess variation and judge how consistent the evidence is
45.A class is evaluating an application of acceleration and motion graphs. Which statement identifies a relevant limitation?
Hard
- AA straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model.
- BAll scientific models reproduce every feature of the real world
- COne favourable result proves that a technology has no disadvantages
- DA conclusion needs no evidence when a scientific term is used
46.Measure a toy trolley's speed at different times as it moves down a low ramp. Which conclusion is most justified by a controlled comparison?
Hard
- AA claim that the result must hold in all possible conditions
- BA conclusion restricted to the tested conditions, with uncertainty and limitations stated
- CA claim that alternative explanations never need testing
- DA claim based only on the most convenient observation
47.Measure a toy trolley's speed at different times as it moves down a low ramp. Select the two practices that strengthen the validity of this comparison.
Medium
- Ause the same ramp angle and release point
- Bchange the measurement method whenever a result is unexpected
- Crecord the trolley's speed in metres per second using the same agreed procedure
- Dreport only observations that confirm the prediction
48.When evaluating evidence about acceleration and motion graphs, select the two scientifically defensible statements.
Hard
- AOne result proves the explanation in every situation
- BA straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model.
- CA conclusion should state the conditions and uncertainty of the evidence
- DModels never need revision when new evidence appears
49.Design a fair investigation for this question: Measure a toy trolley's speed at different times as it moves down a low ramp. Identify what to compare, what to record and one control.
Medium
50.Explain one use of the science in acceleration and motion graphs and evaluate one limitation of the evidence or application.
Hard
51.A trolley's velocity increases from 2.0 m/s to 8.0 m/s in 3.0 s. What is its mean acceleration?
Hard
- A3.3 m/s2
- B18 m/s2
- C2.0 m/s2
- D6.0 m/s2
52.A velocity-time graph is a horizontal line at +4 m/s. Which pair describes the motion?
Hard
- AZero velocity; constant positive acceleration
- BConstant positive velocity; positive acceleration
- CConstant speed; necessarily moving backwards
- DConstant positive velocity; zero acceleration

복습 노트

## Big idea: acceleration and motion graphs - **Key concept: Relationships.** Acceleration is change in velocity divided by time. The gradient of a velocity-time graph gives acceleration and the area beneath it gives displacement. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Motion models help analyse transport and stopping distances. ## Speed & Velocity - **Speed** = distance travelled per unit time; a **scalar** quantity (magnitude only). - Equation: \(v = \frac{s}{t}\), where \(v\) in m/s, \(s\) in m, \(t\) in s. - **Average speed** = total distance / total time; useful when speed varies. - **Velocity** = speed in a given direction; a **vector** quantity (magnitude and direction). - Velocity uses **displacement** (vector) instead of distance. - Same speed but different directions → different velocities. ## Acceleration - **Acceleration** = rate of change of velocity; \(a = \frac{\Delta v}{\Delta t}\), units m/s². - Change in velocity: \(\Delta v = v - u\) (final minus initial). - **Positive acceleration** = speeding up; **negative acceleration (deceleration)** = slowing down. - Any change in velocity (speed up, slow down, change direction) is acceleration. - Formula triangle: cover the quantity to find; \(a = \frac{\Delta v}{\Delta t}\), \(\Delta v = a \times \Delta t\), \(\Delta t = \frac{\Delta v}{a}\). ## Distance-Time Graphs - **Distance-time graph**: straight line = constant speed; horizontal line = stationary. - **Gradient** = speed; steeper slope = faster speed. - Curved line = changing speed (acceleration/deceleration); increasing gradient = speeding up, decreasing = slowing down. - To calculate speed: draw a large gradient triangle, find \(\frac{\Delta y}{\Delta x}\). - Always check units (e.g., km → m, min → s). ## Speed-Time Graphs - **Speed-time graph**: straight line = constant acceleration; horizontal line = constant speed (zero acceleration). - **Gradient** = acceleration; positive gradient = acceleration, negative = deceleration. - **Area under graph** = distance travelled. - Split area into triangles and rectangles: triangle area = \(\frac{1}{2}bh\), rectangle area = \(bh\). - Total distance = sum of all areas under the line. ## Calculating Acceleration from Speed-Time Graphs - For constant acceleration: gradient = \(\frac{\Delta v}{\Delta t}\) using a straight line. - For changing acceleration: draw a **tangent** at the point; gradient of tangent = instantaneous acceleration. - A tangent is a straight line that just touches the curve at that point. - Use a large gradient triangle on the tangent to calculate \(\frac{\Delta y}{\Delta x}\). ## Freefall - In absence of air resistance, all objects fall with same acceleration: **\(g = 9.8 \, \text{m/s}^2\)** (acceleration of freefall). - Weight \(W = mg\), where \(g\) is gravitational field strength (N/kg). - With air resistance: forces are weight (down) and air resistance (up). - Air resistance increases with speed; when it equals weight, resultant force = 0 → **terminal velocity**. - Skydiver: initially accelerates, then air resistance increases, eventually reaches terminal velocity; deploying parachute increases air resistance → deceleration to a lower terminal velocity. - In a vacuum (no air resistance), objects never reach terminal velocity; they accelerate at \(g\) continuously. ## Think like a scientist - Measure a toy trolley's speed at different times as it moves down a low ramp. - **Comparison:** the elapsed time after release. **Outcome:** the trolley's speed in metres per second. - **Control:** use the same ramp angle and release point. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Motion models help analyse transport and stopping distances. - A straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Distance-Time Graphs: **Distance-time graph**: straight line = constant speed; horizontal line = stationary.
Acceleration Calculations: Calculate acceleration using a = Δv/Δt, including positive and negative acceleration (deceleration).
Velocity & Displacement: Distinguish between speed and velocity, and use displacement to calculate velocity.
Speed Calculations: Calculate speed, distance, or time using the equation v = s/t, including unit conversions.
Freefall Motion: Describe the motion of an object in freefall, including acceleration due to gravity and terminal velocity.
Speed-Time Graphs: **Speed-time graph**: straight line = constant acceleration; horizontal line = constant speed (zero acceleration).
Designing scientific inquiries: Plan a fair comparison: Measure a toy trolley's speed at different times as it moves down a low ramp.
Evaluating evidence and impacts: Motion models help analyse transport and stopping distances. A straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model.
Speed & Velocity: **Speed** = distance travelled per unit time; a **scalar** quantity (magnitude only).
Acceleration: **Acceleration** = rate of change of velocity; \(a = \frac{\Delta v}{\Delta t}\), units m/s².
Calculating Acceleration from Speed-Time Graphs: For constant acceleration: gradient = \(\frac{\Delta v}{\Delta t}\) using a straight line.
Freefall: In absence of air resistance, all objects fall with same acceleration: **\(g = 9.8 \, \text{m/s}^2\)** (acceleration of freefall).
Speed: **Speed** = distance travelled per unit time; a **scalar** quantity (magnitude only).
scalar: **Speed** = distance travelled per unit time; a **scalar** quantity (magnitude only).
Average speed: **Average speed** = total distance / total time; useful when speed varies.
Velocity: **Velocity** = speed in a given direction; a **vector** quantity (magnitude and direction).

플래시카드

Which of the following is a scalar quantity?

speed Speed is a scalar quantity because it has magnitude only. Velocity, displacement, and acceleration are vectors as they have both magnitude and direction.

What is the acceleration of free fall near Earth's surface?

9.8 m/s² downward The acceleration of free fall is 9.8 m/s² downward. It is a vector with direction. 9.8 m/s is a speed, not acceleration. 9.8 N/kg is gravitational field strength, which has the same numerical value but different units.

On a distance-time graph, a horizontal line indicates that the object is:

stationary A horizontal line on a distance-time graph means distance is not changing over time, so the object is stationary (speed = 0).

Which of the following is the correct definition of velocity?

Speed in a given direction Velocity is defined as speed in a given direction. It is a vector quantity. Option A is speed, option C is similar but displacement is not the same as speed, option D describes acceleration.

The area under a speed-time graph represents:

distance travelled The area under a speed-time graph gives the distance travelled. Acceleration is given by the gradient.

An object accelerates from 4 m/s to 10 m/s in 3 s. What is its acceleration?

2 m/s² Acceleration = (final velocity - initial velocity) / time = (10 - 4) / 3 = 6 / 3 = 2 m/s².

On a speed-time graph, a straight line with negative gradient represents:

constant deceleration A straight line on a speed-time graph means constant acceleration (or deceleration). A negative gradient means speed is decreasing, so constant deceleration.

A skydiver falls from a plane. After reaching terminal velocity, the parachute opens. Which statement is correct?

The skydiver decelerates to a lower terminal velocity. When the parachute opens, air resistance increases greatly, causing a resultant upward force. The skydiver decelerates and eventually reaches a new, lower terminal velocity.

A car travels at 20 m/s for 5 s, then at 30 m/s for 10 s. What is the total distance travelled?

400 m Distance = area under speed-time graph: first part: 20 m/s × 5 s = 100 m; second part: 30 m/s × 10 s = 300 m; total = 400 m.

A cyclist travels 360 m in 60 s. What is the average speed in m/s?

6 m/s Average speed = distance / time = 360 m / 60 s = 6 m/s.

A car travels along a straight road. The speed-time graph for the car's journey is a straight line from (0 s, 0 m/s) to (10 s, 20 m/s). What is the acceleration of the car?

2 m/s² Acceleration = gradient = change in speed / change in time = (20 - 0) / (10 - 0) = 2 m/s².

The speed-time graph of a skydiver shows a curve that becomes horizontal. What does the horizontal section represent?

The skydiver is moving at terminal velocity A horizontal line on a speed-time graph indicates constant speed. For a skydiver, this is terminal velocity where air resistance equals weight.

A train travels 120 m in 54 s. What is its average speed?

2.22 m/s Average speed = distance / time = 120 m / 54 s = 2.22 m/s (to 2 d.p.).

The speed-time graph of a car consists of a triangle from 0 to 10 s (speed increasing from 0 to 20 m/s) followed by a rectangle from 10 to 30 s (constant speed 20 m/s). What is the total distance travelled?

500 m Distance = area under graph. Triangle area = 0.5 × 10 × 20 = 100 m. Rectangle area = 20 × 20 = 400 m. Total = 500 m.

An object is moving at constant speed in a circle. Which statement about its velocity is correct?

Velocity changes because direction changes Velocity is a vector; it changes when direction changes, even if speed is constant. In circular motion, direction changes continuously.

Which quantity is a vector?

Velocity Velocity has both magnitude and direction, so it is a vector. Speed, distance, and time are scalars.

How would you design the inquiry for acceleration and motion graphs?

Measure a toy trolley's speed at different times as it moves down a low ramp. Compare the elapsed time after release; record the trolley's speed in metres per second; use the same ramp angle and release point.

What limitation matters when applying acceleration and motion graphs?

A straight graph fitted to a few points may hide changing acceleration; collect enough readings to test the model.

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