Starter quiz
- Which of the following are features of a typical displacement–time graph?
- time is shown on the x–axis (horizontal) ✓
- time is shown on the y–axis (vertical)
- displacement is shown on the x–axis (horizontal)
- displacement is shown on the y–axis (vertical) ✓
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- Match the quantity to the correct description.
- displacement⇔a vector measured in m ✓
- velocity⇔a vector measured in m/s ✓
- distance⇔a scalar measured in m ✓
- speed⇔a scalar measured in m/s ✓
- Which of the following are examples of velocity?
- 4 km north
- 3 km/s
- 12 m/s upwards ✓
- 2 mph west ✓
- 100 km/h
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- 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.
- The gradient of the line will be the steepest. ✓
- The gradient of the line will be the shallowest.
- The gradient will be zero (flat).
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- Calculate the speed of a car that travels 500 m in 25 s. Include the unit in your answer.
- '20 m/s' ✓
- 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
- 10 minutes ✓
- 5 minutes
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Exit quiz
- Match the key words and phrases to the correct descriptions.
- displacement–time graph⇔a graph showing distance in a given direction over a period of time ✓
- gradient⇔the steepness of a line or slope ✓
- instantaneous velocity⇔how fast an object moves in a given direction ✓
- average velocity⇔how fast an object moves in a given direction 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 ✓
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- 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
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- 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
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- 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
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- 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.
Worksheet
Presentation
Video
Lesson Details
Key learning points
- The 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 s-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.