Question

A particle moving along a straight line has instantaneous velocities during the first 5 seconds as given below. Draw a velocity-time graph.

Answer 1

Step 1: Given data

In a velocity-time graph, the $x-axis$ is time and the $y-axis$ is velocity.

Therefore, the coordinates of the velocity-time graph are:

1. $(t_0,v_0)=(0s,0m{s}^{-1})$
2. $(t_1,v_1)=(1s,2.5m{s}^{-1})$
3. $(t_2,v_2)=(2s,5m{s}^{-1})$
4. $(t_3,v_3)=(3s,7.5m{s}^{-1})$
5. $(t_4,v_4)=(4s,10m{s}^{-1})$
6. $(t_5,v_5)=(5s,12.5m{s}^{-1})$

Step 2: Plot the graph as per the given data

The velocity-time graph for the given data is plotted below:

The above graph clearly depicts that the velocity is increasing constantly in equal time intervals. Hence, it shows a constant increase in velocity with increasing time.

Thus, the acceleration with which the particle is traveling is a uniform acceleration.

Thus:

The required a velocity-time graph is: