Motion

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Notes

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; used when speed varies.
**Velocity** = speed in a given direction; a **vector** quantity.
Velocity uses **displacement** (vector) instead of distance.
Positive/negative signs indicate direction (e.g., +20 m/s east, −20 m/s west).

Acceleration

**Acceleration** = rate of change of velocity; unit $\frac{m}{s}^{2}$ .
Equation: $a = \frac{\Delta v}{\Delta t}$ where $\Delta v = v - u$ .
Positive acceleration = speeding up; negative acceleration = **deceleration** (slowing down).
Average acceleration useful when acceleration changes.

Distance-Time Graphs

Gradient of a distance–time graph = **speed**.
Straight line = constant speed; horizontal line = stationary.
Steeper gradient = faster speed; curved line = changing speed (acceleration/deceleration).
To calculate speed: draw a large gradient triangle, find $\frac{\Delta y}{\Delta x}$ .

Speed-Time Graphs

Gradient of a speed–time graph = **acceleration**.
Straight line = constant acceleration; horizontal line = constant speed (zero acceleration).
Positive gradient = acceleration; negative gradient = deceleration.
**Area under** a speed–time graph = **distance travelled**.
Calculate area by splitting into triangles and rectangles: $A = \frac{1}{2}bh$ (triangle) or $A = bh$ (rectangle).

Calculating Acceleration from Speed-Time Graphs

For constant acceleration: gradient = $\frac{\Delta v}{\Delta t}$ .
For changing acceleration: draw a **tangent** at the point; gradient of tangent = instantaneous acceleration.
Use a large gradient triangle for accuracy.

Freefall

In absence of air resistance, all objects fall with same **acceleration of freefall** $g = 9.8\,\text{m/s}^2$ .
Velocity increases by 9.8 m/s each second.
Weight $W = mg$ where $g$ is also gravitational field strength (N/kg).

Particle arrangement in solids, liquids, and gases (states of matter).

Practice questions

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1.Which of the following is a scalar quantity?
Easy
- Avelocity
- Bdisplacement
- Cspeed
- Dacceleration
2.Define speed.
Easy
3.A car travels 150 m in 10 s at constant speed. Calculate the speed.
Easy
- A17
- B15
- C16
- D14
4.Velocity is a vector quantity.
Easy
True or false?
5.Complete the sentence.
Medium
The gradient of a distance-time graph represents $the ____ of$ the object.
6.Match each graph shape to the motion it represents.
Medium
- Horizontal line on distance-time graph
- Straight line with positive gradient on speed-time graph
- Curved line on speed-time graph with increasing gradient
- Stationary object
- Constant positive acceleration
- Increasing acceleration
7.Arrange the following speeds in order from slowest to fastest: 10 m/s, 5 m/s, 20 m/s, 15 m/s.
Medium
- 5 m/s
- 10 m/s
- 15 m/s
- 20 m/s
8.A train decelerates from 50 m/s to 42 m/s in 30 s. Calculate the deceleration $(in \frac{m}{s}^{2})$ .
Medium
- A-1.27
- B0.73
- C1.73
- D-0.27

Slides

Speed

Speed is defined as distance travelled per unit time.
It is a scalar quantity (magnitude only, no direction).
For constant speed: $v = s / t$ , where v is speed (m/s), s is distance (m), t is time (s).

Which of the following is a scalar quantity?

Velocity
Speed
Acceleration
Displacement

Average Speed

Average speed = total distance travelled / total time taken.
It is useful when speed varies during a journey.
Example: A hiker's average speed might be 2.0 m/s.

A plane flies at an average speed of 250 m/s for 2 hours. The distance travelled $is ____ m$ .

Velocity

Velocity is speed in a given direction.
It is a vector quantity (magnitude and direction).
Equation: $v = s / t$ , where s is displacement (vector).
Positive/negative signs indicate direction.

Which statement about velocity is correct?

Velocity is a scalar quantity.
Velocity is speed in a given direction.
Velocity is always positive.
Velocity has magnitude only.

Acceleration

Acceleration is the rate of change of velocity.
Equation: $a =$ Δv / Δt, where Δv $= v - u (final -$ initial velocity).
Units: $\frac{m}{s}^{2}$ .
Positive acceleration = speeding up; negative acceleration = slowing down (deceleration).

A train slows from 50 m/s to 42 m/s in 30 s. Its acceleration $is ____ \frac{m}{s}^{2}$ .

Distance-Time Graphs

A distance-time graph shows how distance changes with time.
Gradient = speed.
Straight line = constant speed; horizontal line = stationary; curved line = changing speed (acceleration).

On a distance-time graph, what does a steeper gradient represent?

A slower speed
A faster speed
Zero speed
Deceleration

Speed-Time Graphs

A speed-time graph shows how speed changes with time.
Gradient = acceleration.
Area under the graph = distance travelled.
Straight line = constant acceleration; horizontal line = constant speed.

What does the area under a speed-time graph represent?

Acceleration
Speed
Distance travelled
Time

Calculating Acceleration from Speed-Time Graphs

For a straight line, acceleration = gradient = Δv / Δt.
For a curve, draw a tangent at the point and find its gradient.
The gradient gives instantaneous acceleration.

From a speed-time graph, a cyclist's speed increases from 0 m/s to 5 m/s in 5 s. The acceleration $is ____ \frac{m}{s}^{2}$ .

Freefall

In the absence of air resistance, all objects fall with the same acceleration.
Acceleration of freefall, $g = 9.8 \frac{m}{s}^{2} (near Earth's surface)$ .
Velocity increases by 9.8 m/s every second.

What is the acceleration of freefall near Earth's surface?

$5 \frac{m}{s}^{2}$
$9.8 \frac{m}{s}^{2}$
$10 \frac{m}{s}^{2}$
$0 \frac{m}{s}^{2}$

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