Displacement-Time Graphs

Displacement-time graphs show the displacement of an object from a fixed origin as it moves in a straight line
They show displacement (on the vertical axis) against time (on the horizontal axis)
Displacement-time graphs can go below the horizontal axis whereas distance-time graphs can not
- Distance can not be negative whereas displacement can be

The gradient of the graph equals the velocity of the object
- A positive gradient means the object is travelling forwards
- A negative gradient means that the object is travelling backwards
- The steeper the line, the greater the speed
A straight line shows that the object is moving at a constant velocity
A curved line shows that the object is accelerating or decelerating
A horizontal line shows that the object is stationary
If the graph touches the x-axis, then the object is at the origin at that time

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$Average speed = \frac{Total distance travelled}{Time taken}$

The average speed can not be negative as speed is a scalar quantity and can only take a positive value

$Average velocity = \frac{Displacement from starting point}{Time taken}$

The average velocity is a vector quantity and can be positive, zero or negative

(a) Calculate the velocity of the athlete during the first 2 seconds.

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(b) Describe the motion of the athlete between the times of 2 seconds and 5 seconds.

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(d) Find the total distanced travelled by the athlete during the 14 seconds.

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Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.
Be careful to spot if you are working with a displacement-time graph or a distance-time graph
Check where the graph starts from on the y-axis, the object does not have to start at 0. For example, if the graph starts at 100, the scenario could be a student on a walk starting 100 m from their house.
Distance is a scalar so it can not be negative whereas displacement from a starting point can be.
Think about the units when calculating, make sure they are consistent.

Displacement-Time Graphs (CIE A Level Maths: Mechanics)