Question

The position versus time graph for a certain particle moving along the x-axis is shown in the figure. Find the average velocity in the time intervals (a) 0 to 2 s, (b) 2 s to 4 s, and (c) 4 s to 7 s.

Answer 1

We are given the values of time, but the values of the position are to obtained from the graph corresponding to the given time interval under consideration. We know that the slope of the displacement-time graph represents velocity.
We have, $v_{av}=\frac{x_2-x_1}{t_2-t_1}$
a. Here $x_1=0m,x_2=10m;t_1=0s,t_2=2s.$
Therefore, the required average velocity is given by
$v_{av}=\frac{10-0}{2-0}$ = 5 m/s
b. Here $x_1=10m,x_2=5m;t_1=2s,t_2=4s.$
So the required value of average velocity is given by
$v_{av}=\frac{5-10}{4-2}$ = -2.5 m/s
c. Here $x_1=5m,x_2=-5m;t_1=4s,t_2=7s.$
So the required value of average velocity is given by
$v_{av}=\frac{-5-5}{7-4}$ = -3.3 m/s