 1. Interpreting 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/s² 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 × 1m/s² = 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 − 7 m/s)/9 s = 3.11 m/s² (to 3 significant figures).

3.11 m/s² # 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/s² (to 3 significant figures).

2.08 m/s² End of page