# StudySquare

This page covers the following topics:

1. Interpreting velocity-time graphs

2. Gradient of velocity-time graphs

A velocity-time graph is a graphical representation of an object's motion over a given period of time. The direction and the speed of an object can be deduced from the velocity-time graph of its motion. The area under the velocity-time graph of an object's motion gives its displacement.

The gradient of a velocity-time graph gives the acceleration of an object. A positive gradient shows that the object is accelerating, whereas a negative one shows that it is decelerating.

# 1

The velocity-time graph of an object's motion is drawn as a horizontal line. Explain what this says about the object's motion.

The object is travelling at constant velocity.

constant velocity

# 2

An object is travelling at a constant velocity of 15 m/s for the first 6 seconds of its motion and then it slows down at a constant rate to rest in a further 5 seconds. Draw a velocity-time graph for this object.

The y axis of the graph is velocity in m/s and the x axis is time in seconds.

The object travels at a 15 m/s velocity for 6 seconds.

The object then decelerates to rest in a further 5 seconds.

image

# 3

Plot a labelled velocity-time graph for an object travelling at a constant rate of 17 m/s for 2 seconds and then accelerates for 5 seconds at a rate of 1 m/sĀ² and travels at this new velocity for a further 3 seconds.

The y axis of the graph is velocity in m/s and the x axis is time in seconds.

The object travels at a 17 m/s velocity for 2 seconds.

The object then accelerates to 17 m/s + 5 Ć 1m/sĀ² = 22 m/s in 5 seconds.

The object continues travelling at a constant 22 m/s velocity for another 3 seconds.

image

# 4

Use the given velocity-time graph to calculate the acceleration of the object whose motion it represents.

The acceleration is the gradient of the velocity-time graph.

acceleration = gradient = (35 m/s ā 7 m/s)/9 s = 3.11 m/sĀ² (to 3 significant figures).

3.11 m/sĀ²

# 5

Calculate the acceleration of the object whose velocity-time graph is given to 3 significant figures.

The acceleration is the gradient of the velocity-time graph.

acceleration = gradient = 25 m/s/12 s = 2.08 m/sĀ² (to 3 significant figures).

2.08 m/sĀ²

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