Motion calculations: including complex ones (a=(v–u)/t, v²−u²=2as & v=s/t) | Physics

Starter quiz

Match the quantity to the correct example measurement of it.

distance

⇔

400 m ✓

speed

⇔

80 m/s ✓

acceleration

⇔

20 m/s² ✓
Which of the following statements about motion graphs are correct?

The gradient of a displacement–time graph gives the acceleration.

The gradient of a displacement–time graph gives the velocity. ✓

The gradient of a velocity–time graph gives the acceleration. ✓

The gradient of a velocity–time graph gives the distance travelled.

The gradient of a velocity–time graph gives the speed.
A jogger travels at an average speed of 4.0 m/s. Calculate the time it will take them to travel 1 km.

0.25 s

25 s

250 s ✓

400 s

4000 s
A jet travels a distance of 9000 m in 1 minute. Calculate the speed of the jet in m/s.

667 m/s

9000 m/s

6.67 m/s

150 m/s ✓

300 m/s
A firework rocket is launched from rest and reaches a speed of 20 m/s in 0.25 s. Calculate the acceleration of the rocket.

8 m/s²

5 m/s²

20 m/s²

22.5 m/s²

80 m/s² ✓
An oil tanker increases its velocity from 0.5 m/s to 6.5 m/s in a time of 120 s. Calculate the acceleration of the oil tanker.

5.0 m/s²

0.50 m/s²

0.05 m/s² ✓

0.72 m/s²

720 m/s²

Match the key words or phrases to their definitions.

initial velocity, $u$

⇔

the velocity of an object at the start of a time period ✓

final velocity, $v$

⇔

the velocity of an object at the end of a time period ✓

average velocity

⇔

the rate of change of displacement over a time period ✓

average acceleration

⇔

the rate of change of velocity over a time period ✓
Which of these shows the correct relationship between initial velocity $u$ , final velocity $v$ , acceleration $a$ and distance $s$ ?

$v² – u² = as$

$v² – u² = 2as$ ✓

$v² + u² = 2as$

$v – u = 2as$

$a² – s² = 2vu$
A race car increases its velocity from 12 m/s to 48 m/s in a time of 6.0 s. Calculate the acceleration of race car.

48 m/s²

42 m/s²

8.0 m/s²

6.0 m/s² ✓

288 m/s²
A motorcycle slows with a deceleration of –5.0 m/s² from 25 m/s to a stop. Calculate the distance the motorcycle takes to come to a stop.

31.3 m

125 m

41.7 m

83.3 m

62.5 m ✓
An aeroplane starting from rest needs to reach a take–off velocity of 60 m/s to take off from a runway of length 1500 m. Calculate the minimum acceleration the airplane will need.

0.02 m/s²

4.8 m/s²

2.4 m/s²

1.2 m/s² ✓

3.6 m/s²
A rocket is travelling at 100 m/s away from the Earth. It accelerates with constant acceleration of 0.5 m/s $^2$ . Calculate its new speed after it has accelerated through a distance of 30 km.

141 m/s

158 m/s

200 m/s ✓

250 m/s

300 m/s

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Average velocity = distance travelled ÷ time
Average acceleration = change in velocity ÷ time
Average velocity = (initial velocity + final velocity) ÷ 2
Combining equations for average acceleration and average velocity leads to the equation v² – u² = 2as
Different motion equations can be used to analyse motion based on information provided.

Pupils often apply equations incorrectly or do not spot obvious errors when using them due to not thinking about the science.

Ask pupils to describe what happens for each example in relation to their answers to problems set.

Initial velocity - The initial velocity of an object is the velocity it starts with during a phase of motion.
Final velocity - The final velocity of an object is the velocity it finishes with after a phase of motion.
Average velocity - The average velocity of an object travelling in a straight line is the change in distance divided by the time taken.
Average acceleration - The average acceleration of an object is the change in velocity divided by the time taken.
Uniform acceleration - When the acceleration is constant, it is described as uniform acceleration.