Distance-time graphs

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課程筆記

What is a distance-time graph?

A distance-time graph shows how far an object has travelled over time.
Time is plotted on the x-axis (horizontal) and distance on the y-axis (vertical).
The gradient (steepness) of the line represents the speed of the object.
A steeper gradient means a greater speed.

Calculating speed from the gradient

Gradient = change in distance ÷ change in time = Δy / Δx.
This is the same as the speed equation: speed = distance ÷ time.
Example: A jogger travels 25 m in 5 s → speed = 25 ÷ 5 = 5 m/s.
Another jogger travels 25 m in 10 s → speed = 25 ÷ 10 = 2.5 m/s.

Interpreting different shapes

A straight, sloping line indicates constant speed.
A horizontal line means the object is stationary (not moving).
A curved line shows changing speed (acceleration or deceleration).
If the gradient decreases over time, the object is decelerating (slowing down).
If the gradient increases over time, the object is accelerating (speeding up).

Comparing speeds on the same graph

When two lines are plotted, the steeper line corresponds to the faster object.
You can compare speeds by calculating the gradient of each line.
The line with the larger gradient has the higher speed.

Distance-time graph comparing two joggers. The steeper blue line shows a higher speed (5 m/s) than the red line (2.5 m/s).

Curved distance-time graphs: the blue curve (decreasing gradient) shows deceleration; the red curve (increasing gradient) shows acceleration.

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練習題

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1.What does the gradient of a distance-time graph represent?
Easy
- ASpeed
- BAcceleration
- CDistance
- DTime
2.What is the equation for speed?
Easy
- ASpeed = Distance × Time
- BSpeed = Distance ÷ Time
- CSpeed = Time ÷ Distance
- DSpeed = Distance + Time
3.A jogger runs 25 m in 5 s. What is their speed?
Easy
- A5 m/s
- B0.2 m/s
- C125 m/s
- D30 m/s
4.A jogger runs 25 m in 10 s. What is their speed?
Easy
- A2.5 m/s
- B0.4 m/s
- C250 m/s
- D15 m/s
5.In a distance-time graph, a steeper gradient indicates:
Easy
- AGreater speed
- BLower speed
- CConstant speed
- DZero speed
6.On a distance-time graph, a horizontal line indicates:
Easy
- AThe object is stationary
- BThe object is moving at constant speed
- CThe object is accelerating
- DThe object is decelerating
7.What does a decreasing gradient on a distance-time graph represent?
Medium
- ADeceleration
- BAcceleration
- CConstant speed
- DStationary object
8.What does an increasing gradient on a distance-time graph represent?
Medium
- AAcceleration
- BDeceleration
- CConstant speed
- DStationary object

更多題目

9.A distance-time graph shows a straight line from (0,0) to (4,20). What is the speed?
Medium
- A5 m/s
- B0.2 m/s
- C80 m/s
- D24 m/s
10.A distance-time graph has a line that curves upwards (increasing gradient). This represents:
Medium
- AAcceleration
- BDeceleration
- CConstant speed
- DStationary
11.A distance-time graph shows a line that is straight and sloping upwards. Which statement is true?
Easy
- AThe object is moving at constant speed
- BThe object is accelerating
- CThe object is decelerating
- DThe object is stationary
12.What does the vertical axis of a distance-time graph measure?
Easy
- ADistance
- BTime
- CSpeed
- DAcceleration
13.A cyclist travels at a constant speed. Which distance-time graph represents the cyclist's motion?
Easy
- AA straight line sloping upwards from the origin
- BA horizontal line
- CA curve that becomes steeper over time
- DA straight line sloping downwards
14.A car travels 150 m in 10 s. What is its speed?
Easy
- A15 m/s
- B1500 m/s
- C0.067 m/s
- D1.5 m/s
15.A distance-time graph shows a line that starts steep and becomes less steep over time. What does this represent?
Medium
- ADeceleration
- BAcceleration
- CConstant speed
- DStationary object
16.A runner's distance-time graph shows a straight line from (0,0) to (8,40) and then a horizontal line from (8,40) to (12,40). What is the runner's speed during the first 8 seconds?
Medium
- A5 m/s
- B40 m/s
- C3.33 m/s
- D10 m/s
17.Two objects A and B have distance-time graphs. Graph A has a steeper gradient than graph B. Which statement is correct?
Easy
- AA is faster than B
- BB is faster than A
- CA has travelled further than B
- DB has travelled further than A
18.A distance-time graph shows a horizontal line. What is the object doing?
Easy
- AStationary
- BMoving at constant speed
- CAccelerating
- DDecelerating
19.A student measures the distance a toy car travels every 2 seconds. The results are: 0 s: 0 m, 2 s: 4 m, 4 s: 8 m, 6 s: 12 m. What is the speed of the car?
Medium
- A2 m/s
- B4 m/s
- C0.5 m/s
- D1 m/s
20.A distance-time graph has a curved line that gets steeper. What does this indicate about the object's motion?
Medium
- AThe object is accelerating
- BThe object is decelerating
- CThe object is moving at constant speed
- DThe object is stationary
21.A train travels 300 m in 15 s, then stops for 5 s, then travels another 200 m in 10 s. What is the total distance travelled?
Medium
- A500 m
- B300 m
- C200 m
- D600 m
22.A distance-time graph for a car shows a straight line from (0,0) to (5,100). What is the speed of the car?
Medium
- A20 m/s
- B100 m/s
- C5 m/s
- D0.05 m/s
23.A distance-time graph shows a line that goes up, then horizontal, then up again. What does this represent?
Medium
- AMoving, then stationary, then moving again
- BConstant speed throughout
- CAccelerating, then constant speed, then decelerating
- DDecelerating, then stationary, then accelerating
24.In an experiment to measure the speed of a toy car, a student records the distance travelled every 0.5 s. Which of the following is the most appropriate method to ensure accurate results?
Medium
- AUse a ruler to measure distance and a stopwatch to measure time, repeating the experiment three times and calculating the mean speed.
- BEstimate the distance by eye and use a stopwatch, taking one measurement only.
- CUse a tape measure and a stopwatch, but only record one set of readings.
- DMeasure the distance with a ruler and time with a pendulum clock.
25.A student plots a distance-time graph for a moving object. The graph shows a straight line from (0,0) to (4,20) and then a curved line that becomes less steep from (4,20) to (8,30). Which statement correctly describes the motion?
Hard
- AThe object moves at constant speed for 4 seconds, then decelerates.
- BThe object accelerates for 4 seconds, then moves at constant speed.
- CThe object moves at constant speed for 4 seconds, then accelerates.
- DThe object decelerates for 4 seconds, then moves at constant speed.
26.In an experiment to investigate motion, a student uses a ticker timer to record the position of a trolley at regular intervals. The tape produced shows dots that are evenly spaced. What does this indicate about the motion?
Easy
- AThe trolley is moving at constant speed.
- BThe trolley is accelerating.
- CThe trolley is decelerating.
- DThe trolley is stationary.
27.A car travels at a constant speed of 10 m/s for 5 seconds, then decelerates uniformly to rest over the next 5 seconds. Which distance-time graph best represents this motion?
Hard
- AA straight line from (0,0) to (5,50) followed by a curve that becomes less steep and ends horizontal at (10,75).
- BA straight line from (0,0) to (5,50) followed by a straight line with negative gradient to (10,0).
- CA curve that is steep at the start and becomes less steep from (0,0) to (10,50).
- DA straight line from (0,0) to (10,100).
28.A student measures the distance a ball rolls down a ramp every 0.2 seconds. The results are: 0.0 s: 0.0 m, 0.2 s: 0.1 m, 0.4 s: 0.4 m, 0.6 s: 0.9 m. What can be concluded about the ball's motion?
Medium
- AThe ball is accelerating.
- BThe ball is moving at constant speed.
- CThe ball is decelerating.
- DThe ball is stationary.
29.Which of the following is the correct method to calculate the speed from a distance-time graph at a specific instant?
Medium
- ADraw a tangent to the curve at that instant and calculate its gradient.
- BCalculate the gradient of the line between the start and that point.
- CMeasure the slope of the line from the origin to that point.
- DFind the area under the graph up to that time.
30.A student records the distance travelled by a toy car every second and plots a distance-time graph. The graph is a straight line from (0,0) to (5,25). The student then repeats the experiment but the car moves at half the speed. Which graph represents the second experiment?
Medium
- AA straight line from (0,0) to (5,12.5).
- BA straight line from (0,0) to (10,25).
- CA straight line from (0,0) to (2.5,25).
- DA straight line from (0,0) to (5,25) but with a dashed line.
31.In a distance-time graph, the gradient is calculated as change in distance divided by change in time. What is the unit of the gradient?
Easy
- Am/s
- Bm s
- Cs/m
- Dm/s²
32.A distance-time graph shows two lines: line A passes through (0,0) and (4,20); line B passes through (0,0) and (4,10). Which statement is correct?
Medium
- ALine A represents a speed of 5 m/s and line B represents 2.5 m/s.
- BLine A represents a speed of 20 m/s and line B represents 10 m/s.
- CLine A represents a speed of 4 m/s and line B represents 2 m/s.
- DLine A represents a speed of 0.2 m/s and line B represents 0.4 m/s.
33.On a distance-time graph, a horizontal line represents:
Easy
- AThe object is stationary.
- BThe object is moving at constant speed.
- CThe object is accelerating.
- DThe object is decelerating.
34.A student uses a motion sensor to collect data for a ball thrown vertically upwards. The distance-time graph for the ball's upward and downward journey is a curve. Which statement about the gradient of the graph at the highest point is correct?
Medium
- AThe gradient is zero, indicating the ball is momentarily stationary.
- BThe gradient is maximum, indicating the ball is moving fastest.
- CThe gradient is negative, indicating the ball is moving downwards.
- DThe gradient is positive, indicating the ball is moving upwards.
35.A student calculates the speed of a runner from a distance-time graph. The graph shows a straight line from (0,0) to (10,100). The student misreads the axes and thinks the time is on the vertical axis. What speed would they calculate?
Medium
- A0.1 m/s
- B10 m/s
- C100 m/s
- D1000 m/s
36.A distance-time graph shows a straight line from (0,0) to (6,30). What is the speed of the object?
Easy
- A5 m/s
- B6 m/s
- C30 m/s
- D0.2 m/s
37.A distance-time graph for a car shows a curve that becomes steeper over time. What does this indicate about the car's motion?
Easy
- AThe car is moving at constant speed.
- BThe car is decelerating.
- CThe car is accelerating.
- DThe car is stationary.
38.A student plots a distance-time graph for a ball rolling down a ramp. The graph is a curve that becomes less steep over time. What does this tell you about the ball's motion?
Easy
- AThe ball is accelerating.
- BThe ball is decelerating.
- CThe ball is moving at constant speed.
- DThe ball is stationary.
39.In a distance-time graph, what does a horizontal line represent?
Easy
- AConstant speed
- BAcceleration
- CDeceleration
- DStationary object
40.Two distance-time graphs are drawn on the same axes. Graph A has a steeper gradient than Graph B. What can you conclude?
Easy
- AGraph A represents a higher speed than Graph B.
- BGraph A represents a lower speed than Graph B.
- CGraph A represents a stationary object.
- DGraph A represents deceleration.
41.The gradient of a distance-time graph represents the speed of the object.
Easy
True or false?
42.A horizontal line on a distance-time graph indicates the object is moving at constant speed.
Easy
True or false?
43.On a distance-time graph, what does a horizontal line represent?
Easy
- AConstant speed
- BAccelerating
- CStationary
- DDecelerating
44.An increasing gradient on a distance-time graph indicates the object is accelerating.
Easy
True or false?
45.A decreasing gradient on a distance-time graph indicates the object is decelerating.
Easy
True or false?
46.Which statement about the gradient of a distance-time graph is correct?
Medium
- AIt is calculated as change in time divided by change in distance.
- BIt gives the acceleration of the object.
- CIt gives the speed of the object.
- DIt is always constant for any motion.
47.Match each description of motion to the correct shape on a distance-time graph.
Medium
- Constant speed
- Stationary
- Accelerating
- Decelerating
- Straight line sloping upwards
- Horizontal line
- Curve getting steeper
- Curve getting less steep
48.Arrange the following steps in the correct order to calculate the speed from a distance-time graph.
Medium
- Measure the change in distance (Δy)
- Measure the change in time (Δx)
- Calculate gradient = Δy / Δx
- Identify the straight line segment on the graph
49.A distance-time graph shows a straight line from (0,0) to (10,50). Which of the following statements are correct? (Select all that apply)
Medium
- AThe speed is 5 m/s
- BThe object is accelerating
- CThe object is moving at constant speed
- DThe gradient is 5
- EThe object is stationary
50.On a distance-time graph, a steeper gradient always indicates a higher speed.
Easy
True or false?
51.Complete the sentence.
Easy
On a distance-time graph, the steeper the gradient, the ____ the speed.
52.A jogger travels 25 m in 5 s. Calculate their speed.
Easy
53.A jogger travels 25 m in 10 s. Calculate their speed.
Easy
54.State what the gradient of a distance-time graph represents.
Easy
55.A jogger runs 30 m in 6 s. Calculate their speed in m/s.
Easy
56.Complete the sentence using the words: gradient, speed, distance, time.
Easy
The ____ of a distance-time graph represents the ____ of the object.
57.State the equation that links speed, distance and time.
Easy
58.A jogger travels 25 m in 5 s. Calculate their speed.
Easy
- A6 m/s
- B4 m/s
- C5 m/s
- D7 m/s
59.A jogger travels 25 m in 10 s. Calculate their speed.
Easy
- A1.5 m/s
- B3.5 m/s
- C2.5 m/s
- D4.5 m/s
60.A jogger runs 30 m in 6 s. Calculate their speed in m/s.
Easy
- A5 m/s
- B7 m/s
- C4 m/s
- D6 m/s

複習筆記

## Distance-Time Graphs - **Purpose**: Represent the journey of a moving object. - **Gradient (steepness)** = speed. Steeper gradient = greater speed. - **Calculating gradient**: \[ \text{gradient} = \frac{\Delta y}{\Delta x} \] For distance-time graphs, Δy = distance travelled, Δx = time taken. - **Speed equation**: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] - **Examples**: - Faster jogger: 25 m in 5 s → speed = 5 m/s. - Slower jogger: 25 m in 10 s → speed = 2.5 m/s. - **Changing speed**: - **Decelerating**: gradient decreasing over time. - **Accelerating**: gradient increasing over time.

Distance-time graph: A graph showing the distance travelled by an object over time.
Gradient: The steepness of a line on a graph; for distance-time graphs, gradient = speed.
Speed: Distance travelled per unit time; calculated as distance ÷ time.
Acceleration: Increase in speed over time; shown by increasing gradient on a distance-time graph.
Deceleration: Decrease in speed over time; shown by decreasing gradient on a distance-time graph.

字卡

What does the gradient of a distance-time graph represent?

The gradient represents the speed of the object.

How is the gradient of a distance-time graph calculated?

Gradient = change in distance (Δy) divided by change in time (Δx).

What does a steeper gradient on a distance-time graph indicate?

A steeper gradient indicates a greater speed.

What is the equation for speed?

Speed = Distance ÷ Time.

A jogger travels 25 m in 5 s. Calculate their speed.

Speed = 25 m ÷ 5 s = 5 m/s.

A jogger travels 25 m in 10 s. Calculate their speed.

Speed = 25 m ÷ 10 s = 2.5 m/s.

What does a decreasing gradient over time on a distance-time graph indicate?

It indicates the object is decelerating (slowing down).

What does an increasing gradient over time on a distance-time graph indicate?

It indicates the object is accelerating (speeding up).

On a distance-time graph, what does a horizontal line represent?

A horizontal line represents the object is stationary (not moving).

On a distance-time graph, what does a straight diagonal line represent?

A straight diagonal line represents constant speed.

What is the symbol for change in distance?

Δy or Δd.

What is the symbol for change in time?

Δx or Δt.

What does a curved line on a distance-time graph indicate?

A curved line indicates changing speed (acceleration or deceleration).

If two objects have distance-time graphs, how can you tell which is faster?

The object with the steeper gradient (line) is faster.

What are the axes of a distance-time graph?

Distance on the y-axis (vertical) and time on the x-axis (horizontal).

What does a flat (horizontal) section on a distance-time graph mean?

The object is not moving; it is at rest.

How do you calculate speed from a distance-time graph?

Speed = gradient = (change in distance) / (change in time).

What does a straight line with positive slope on a distance-time graph show?

It shows constant speed in a straight line away from the start.

What does a straight line with negative slope on a distance-time graph show?

It shows constant speed returning towards the start (decreasing distance).

What is the speed of an object that travels 50 m in 10 s?

Speed = 50 m ÷ 10 s = 5 m/s.

What does a curve that gets steeper over time indicate?

It indicates acceleration (increasing speed).

What does a curve that gets less steep over time indicate?

It indicates deceleration (decreasing speed).

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