New
New
Year 10
AQA
Higher

# Calculating from motion graphs: including displacement (a=Δv/t and v=s/t)

I can take readings from motion graphs to calculate distance, displacement, speed, velocity and acceleration.

New
New
Year 10
AQA
Higher

# Calculating from motion graphs: including displacement (a=Δv/t and v=s/t)

I can take readings from motion graphs to calculate distance, displacement, speed, velocity and acceleration.

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## Lesson details

### Key learning points

1. Acceleration is equal to the gradient of a velocity-time graph.
2. A falling line shows decreasing velocity called deceleration, which is a negative acceleration.
3. Instantaneous speed at a point on a displacement-time graph equals the gradient of a tangent at that point .
4. The distance travelled is equal to the area under a velocity-time graph.
5. Displacement is equal to the net positive area under a velocity-time graph.

### Common misconception

Pupils often confuse displacement–time graphs with velocity–time graphs.

Emphasise the need for pupils to always read the axes of a graph first, before they start to think about any lines drawn on it.

### Keywords

• Displacement-time graph - A displacement–time graph shows the displacement of an object over a period of time.

• Velocity-time graph - A velocity–time graph shows the velocity of an object over a period of time.

• Velocity - The velocity of an object is the rate of change of displacement. This is how fast it is moving in a particular direction.

• Acceleration - The acceleration of an object is the rate of change of velocity. This is how much the velocity changes per second.

Use a wide variety of movement graphs, allowing pupils to identify the key information. Link these to real objects via video clips showing constant velocity, acceleration, deceleration and so on.
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).

## Starter quiz

### 6 Questions

Q1.
Match the quantity to the unit it is measured in.

kilogram (kg)

metres per second (m/s)

metres (m)

Correct Answer:acceleration,metres per second squared (m/s\$\$^2\$\$)

metres per second squared (m/s\$\$^2\$\$)

Q2.
What is the velocity of this object at time = 3 s?
1 m/s
3 m/s
5 m/s
6 m/s
9 m/s
Q3.
Which of these is a correct definition of acceleration?
The rate of change of displacement.
Correct answer: The rate of change of velocity.
The rate of change of speed.
The overall change in velocity.
The overall change in position.
Q4.
During which time period is this object decelerating?
Between 0 s and 2 s.
Between 2 s and 4 s.
Between 4 s and 7 s.
Correct answer: Between 5 s and 7 s.
Between 7 s and 8 s.
Q5.
A speedboat increases its velocity from 2.0 m/s to 14 m/s in a time of 8.0 s. Calculate the acceleration of the speedboat.
0.25 m/s\$\$^2\$\$
0.67 m/s\$\$^2\$\$
1.75 m/s\$\$^2\$\$
12 m/s\$\$^2\$\$
Q6.
The displacement-time graph shows the movement of a robot. Calculate the velocity of the robot at time = 45 s.

## Exit quiz

### 6 Questions

Q1.
Match the key words and phrases to their explanations.
Correct Answer:displacement-time graph,this shows the displacement of an object over a period of time

this shows the displacement of an object over a period of time

Correct Answer:velocity-time graph,this shows the velocity of an object over a period of time

this shows the velocity of an object over a period of time

Correct Answer:acceleration,the rate of change of velocity

the rate of change of velocity

Correct Answer:velocity ,the rate of change of displacement

the rate of change of displacement

Q2.
The graph shows the movement of a van over time. Find the total distance travelled for the journey.
20 km
30 km
50 km
70 km
Q3.
The graph shows the movement of a van making two deliveries. Find the average speed of the van during the outwards journey, from 0 to 3 hours.
0.6 km/h
10 m/s
10 km/h
17 m/s
Q4.
The graph shows the displacement of a dynamics trolley along a bench. Calculate the velocity of the trolley at time = 2 s.
0.16 m/s