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

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

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

A tangent drawn to the gradient on a curving displacement-time graph will give the instantaneous velocity.

Calculating from displacement-time graphs: including tangents (v=x/t)

Combined science

In the Energy of moving objects unit, they will build on this knowledge to learn how to calculate the amount of energy of objects have because they are moving, stretched or in a gravitational field; and to calculate energy transfers using knowledge of energy conservation and dissipation.

In the Moving by force unit, pupils learnt how to calculate speed and describe motion using distance-time graphs, apply Newton’s first law of motion and calculate the amount of energy needed to move an object to a new position.

Measuring and calculating motion

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

how fast an object moves in a given direction

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

Match the key words and phrases to the correct descriptions.

the total distance they travelled was 6 m

the total distance they travelled was 18 m 

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 figure shows a displacement-time graph.
What is the total distance travelled during the 50 s?

The figure shows a displacement-time graph.
Calculate the average velocity for the first 20 s.

The figure shows a displacement-time graph.
Calculate the average velocity between 30 s and 50 s.

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

Find the changes in displacement and time between the points.

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

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.

time is shown on the x–axis (horizontal)

displacement is shown on the x–axis (horizontal)

displacement is shown on the y–axis (vertical)

Which of the following are features of a typical displacement–time graph?

Match the quantity to the correct description.

Which of the following are examples of velocity?

The displacement will be at its maximum value.

The gradient of the line will be the steepest.

The gradient of the line will be the shallowest.

Which of the following features of a displacement–time graph indicates an object travelling at the greatest speed?

Calculate the speed of a car that travels 500 m in 25 s. 
Include the unit in your answer.

How long will a fish travelling at 2.5 m/s take to travel 1.5 km?

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