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

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.
Tangent - A tangent drawn to the gradient on a curving displacement-time graph will give the instantaneous velocity.
Instantaneous velocity - The instantaneous velocity is the velocity of an object at a particular moment in time.

Pupils often struggle with negative displacement and with negative velocity. Help the pupils select a direction as positive using as many examples with 'opposite' directions as possible. Show the pupils the graphs and answers that would result if they had chosen the opposite direction as positive.

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).

Video

Skip video

Worksheet

Download worksheet

Skip worksheet

Starter quiz

Download 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?

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

Download 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 total 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.

Starting with the first step, put these stages in order to explain how to find the instantaneous speed of an object with changing velocity from a displacement-time graph.

1 - Draw a tangent to the curve at the time the velocity is needed for.

2 - Select two points along the tangent.

3 - Find the changes in displacement and time between the points.

4 - Calculate velocity using velocity = change in displacement ÷ change in time.