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Year 10
AQA
Higher

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

I can choose and use different equations to calculate different motions.

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Year 10
AQA
Higher

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

I can choose and use different equations to calculate different motions.

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Lesson details

Key learning points

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

Keywords

  • 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.

Common misconception

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.

Pupils become confused about which equation to use or which symbol represents which quantity. Take time to go through each calculation carefully, using word equations if these help the pupils; they do not need to use symbols in examinations to score full marks.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Match the quantity to the correct example measurement of it.
Correct Answer:distance,400 m

400 m

Correct Answer:speed,80 m/s

80 m/s

Correct Answer:acceleration,20 m/s²

20 m/s²

Q2.
Which of the following statements about motion graphs are correct?
The gradient of a displacement–time graph gives the acceleration.
Correct answer: The gradient of a displacement–time graph gives the velocity.
Correct answer: 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.
Q3.
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
Correct answer: 250 s
400 s
4000 s
Q4.
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
Correct answer: 150 m/s
300 m/s
Q5.
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
Correct answer: 80 m/s²
Q6.
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
Correct answer: 0.05 m/s²
0.72 m/s²
720 m/s²

Exit quiz

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6 Questions

Q1.
Match the key words or phrases to their definitions.
Correct Answer:initial velocity, $$u$$,the velocity of an object at the start of a time period

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

Correct Answer:final velocity, $$v$$,the velocity of an object at the end of a time period

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

Correct Answer:average velocity,the rate of change of displacement over a time period

the rate of change of displacement over a time period

Correct Answer:average acceleration,the rate of change of velocity over a time period

the rate of change of velocity over a time period

Correct Answer:$$Δv$$ ,the change in velocity

the change in velocity

Q2.
Which of these shows the correct relationship between initial velocity $$u$$, final velocity $$v$$, acceleration $$a$$ and distance $$s$$?
$$v² – u² = as$$
Correct answer: $$v² – u² = 2as$$
$$v² + u² = 2as$$
$$v – u = 2as$$
$$a² – s² = 2vu$$
Q3.
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
Correct answer: 6.0 m/s²
288 m/s²
Q4.
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
Correct answer: 62.5 m
Q5.
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 aeroplane will need.
0.02 m/s²
4.8 m/s²
2.4 m/s²
Correct answer: 1.2 m/s²
3.6 m/s²
Q6.
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
Correct answer: 200 m/s
250 m/s
300 m/s