Describing Motion

Speed & Velocity

Speed is a measure of how fast or slow an object is moving
It is a scalar quantity
- Because it only contains a magnitude (without a direction)

The velocity of a moving object is similar to its speed, except it also describes the object’s direction
Velocity is a vector quantity
- The velocity of an object contains both magnitude and direction
- e.g. ‘15 m / s south’ or ‘250 mph on a bearing of 030°’
Comparing Speed and Velocity

Speed & Velocity, downloadable IGCSE & GCSE Physics revision notes

The cars in the diagram above have the same speed (a scalar quantity) but different velocities (a vector quantity). Fear not, they are in different lanes!

Acceleration

Acceleration is defined as the rate of change of velocity
In other words, it describes how much an object's velocity changes every second
The acceleration of an object can be positive or negative, depending on whether the object is speeding up or slowing down
- If an object is speeding up, its acceleration is positive
- If an object is slowing down, its acceleration is negative (sometimes called deceleration)

Positive and Negative Acceleration

Acceleration Examples, downloadable IGCSE & GCSE Physics revision notes

A rocket speeding up (accelerating) and a car slowing down (decelerating)

Calculating Speed & Acceleration

Calculating Speed

For objects that are moving with a constant speed, use the equation below to calculate the speed:

$Speed = \frac{distance}{time}$

Where:
- Speed is measured in metres per second (m/s)
- Distance travelled is measured in metres (m)
- Time taken is measured in seconds (s)

The Speed of Different Objects

Person vs Bee, downloadable IGCSE & GCSE Physics revision notes

A hiker might have a speed of 2.0 m/s, whereas a particularly excited bumble bee can have a speed of up to 4.5 m/s

Calculating Acceleration

The equation below is used to calculate the average acceleration of an object:

$acceleration = \frac{change in velocity}{change in time}$

$a = \frac{∆ v}{∆ t}$

Where:
- a = acceleration in metres per second squared (m/s²)
- Δv = change in velocity in metres per second (m/s)
- Δt = time taken in seconds (s)

Worked example

Planes fly at typical speeds of around 250 m/s. Calculate the total distance travelled by a plane moving at this average speed for 2 hours.

Answer:

Step 1: List the known quantities

Average speed = 250 m/s
Time taken = 2 hours

Step 2: Write the relevant equation

$Speed = \frac{distance}{time}$

Step 3: Rearrange for the total distance

total distance = average speed × time taken

Step 4: Convert any units

The time given in the question is not in standard units
Convert 2 hours into seconds:

2 hours = 2 × 60 × 60 = 7200 s

Step 5: Substitute the values for average speed and time taken

total distance = 250 × 7200

total distance = 1 800 000 m

Worked example

A Japanese bullet train decelerates at a constant rate in a straight line. The velocity of the train decreases from 50 m/s to 42 m/s in 30 seconds.

(a)

Calculate the change in velocity of the train.

(b)

Calculate the deceleration of the train, and explain how your answer shows the train is slowing down.

Answer:

Part (a)

Step 1: List the known quantities

Initial velocity = 50 m/s
Final velocity = 42 m/s

Step 2: Write the relevant equation

change in velocity = final velocity − initial velocity

Step 3: Substitute values for final and initial velocity

change in velocity = 42 − 50

change in velocity = −8 m/s

Part (b)

Step 1: List the known quantities

Change in velocity, Δv = − 8 m/s
Time taken, t = 30 s

Step 2: Write the relevant equation

$a = \frac{∆ v}{∆ t}$

Step 3: Substitute the values for change in velocity and time

a = −8 ÷ 30

a = −0.27 m/s

Step 4: Interpret the value for deceleration

The answer is negative, which indicates the train is slowing down

Examiner Tip

Remember the units for acceleration are metres per second squared, m/s². In other words, acceleration measures how much the velocity (in m/s) changes every second, m/s/s.

Describing Motion (WJEC GCSE Physics)

Revision Note