New
New
Year 10
AQA
Foundation

# Calculating from displacement-time graphs (v=s/t)

I can take readings from displacement-time graphs to find distance, displacement, speed and velocity.

New
New
Year 10
AQA
Foundation

# Calculating from displacement-time graphs (v=s/t)

I can take readings from displacement-time graphs to find distance, displacement, speed and velocity.

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## Lesson details

### Key learning points

1. Velocity of an object is equal to the gradient of a displacement-time graph.
2. A direction in which velocity and displacement are measured needs to be chosen.
3. A negative gradient on a displacement-time graph (sloping downwards) represents velocity in the opposite direction.
4. A negative value for displacement represents a position ‘behind’ the starting position.

### Common misconception

A pair of coordinates on a d-t graph can be used to calculate the instantaneous speed or velocity at that point, but that only works for a straight line graph through the origin.

Ask pupils to calculate the velocity of a graph that represents a steady velocity on a line that does not go through the origin, and to check to see if dividing the values at any point on the line gives the right value for velocity.

### Keywords

• Displacement-time graph - A displacement-time graph shows the change in displacement over a time period. The displacement along a straight line can be positive or negative.

• Gradient - The gradient on a displacement-time graph gives the instantaneous velocity.

• Instantaneous velocity - The instantaneous velocity is the velocity of an object at a particular moment in time.

### 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.
Which of the following are features of a typical displacement–time graph?
Correct answer: time is shown on the x–axis (horizontal)
time is shown on the y–axis (vertical)
displacement is shown on the x–axis (horizontal)
Correct answer: displacement is shown on the y–axis (vertical)
Q2.
Match the quantity to the correct description.
Correct Answer:displacement,a vector measured in m

a vector measured in m

Correct Answer:velocity,a vector measured in m/s

a vector measured in m/s

Correct Answer:distance,a scalar measured in m

a scalar measured in m

Correct Answer:speed,a scalar measured in m/s

a scalar measured in m/s

Q3.
Which of the following are examples of velocity?
Correct answer: 4 km north
3 km/s
Correct answer: 12 m/s upwards
Correct answer: 2 mph west
100 km/h
Q4.
Which of the following features of a displacement–time graph indicates an object travelling at the greatest speed?
The time will be at its maximum value.
The displacement will be at its maximum value.
Correct answer: The gradient of the line will be the steepest
The gradient of the line will be the shallowest.
The gradient will be zero (flat).
Q5.
Calculate the speed of a car that travels 500 m in 25 s. Include the unit in your answer.
Correct Answer: 20 m/s, 20 metres per second, 20 m/sec, 20 metres/s
Q6.
How long will a fish travelling at 2.5 m/s take to travel 1.5 km?
0.6 minutes
1 minutes
3.75 minutes
Correct answer: 10 minutes
5 minutes

## Exit quiz

### 6 Questions

Q1.
Match the key words and phrases to the correct descriptions.
Correct Answer:displacement–time graph,a graph showing distance in a given direction over a period of time

a graph showing distance in a given direction over a period of time

Correct Answer:gradient,the steepness of a line or slope

the steepness of a line or slope

Correct Answer:instantaneous velocity,how fast an object moves in a given direction

how fast an object moves in a given direction

Correct Answer:average velocity,how fast an object moves in a given direction over a period of time

how fast an object moves in a given direction over a period of time

Q2.
A pupil follows these movement instructions: move 5 m left, then 4 m left, then 6 m right and finally 3 m left. Which of the following statements are correct?
the final displacement is 18 m left
Correct answer: the final displacement is 6 m left
the total distance they travelled was 6 m
Correct answer: the distance they travelled was 18 m
Q3.
The figure shows a displacement-time graph. What is the total distance travelled during the 50 s?
2 m
5 m
6 m
Correct answer: 8 m
10 m
Q4.
The figure shows a displacement-time graph. Calculate the average velocity for the first 20 s.
Correct answer: 0.15 m/s
1.5 m/s
3.0 m/s
6.7 m/s
20 m/s
Q5.
The figure shows a displacement-time graph. Calculate the average velocity between 30 s and 50 s.
0.04 m/s
-0.04 m/s
0.15 m/s
Correct answer: -0.15 m/s
-25 m/s
Q6.
The figure shows a displacement time graph. At which of these times is the speed greatest?
0 s
10 s
Correct answer: 15 s
30 s
40 s