Calculating from displacement-time graphs: including tangents (v=s/t) | Exit Quiz | Oak National Academy

Match the key words and phrases to the correct descriptions.

• instantaneous velocity

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

• displacement–time graph

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

• average velocity

• the steepness of a line or slope

• gradient

• how fast an object moves in a given direction

Answer explanation

A displacement–time graph shows distance in a direction over a period of time, the gradient of the line is a measure of its steepness, instantaneous velocity is the velocity at a given moment while average velocity is velocity over a period of time.

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

• the final displacement is 6 m left

• the total distance they travelled was 6 m

• the total distance they travelled was 18 m

Answer explanation

The total distance travelled was 5 m + 4 m + 6 m + 3 m = 18 m The final displacement was 5 m + 4 m – 6 m + 3 m = 6 m (left)

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

• 2 m

• 5 m

• 6 m

• 8 m

• 10 m

Answer explanation

The total distance travelled is 5 m forwards and then 3 m backwards, making a total of 8 m.

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

• 0.15 m/s

• 1.5 m/s

• 3.0 m/s

• 6.7 m/s

• 20 m/s

Answer explanation

The displacement is 3 m at 20 s. velocity = change in displacement ÷ time = 3 m ÷ 20 s = 0.15 m/s

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

• -0.15 m/s

• -25 m/s

Answer explanation

The change in displacement is 2 m – 5 m = -3 m. The change in time is 50 – 30 s = 20 s velocity = change in displacement ÷ time = -3 m ÷ 20 s = -0.15 m/s

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.

• Select two points along the tangent.

• Find the changes in displacement and time between the points.

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

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

Answer explanation

The velocity is found by drawing a tangent and then finding the gradient using: velocity (gradient) = change in displacement ÷ change in time.