Question

From the velocity-time plot shown in figure (3−E5), find the distance travelled by the particle during the first 40 seconds. Also find the average velocity during this period.
Figure

Answer 1

The average velocity during this period is zero, as the displacement is zero.

Explanation:

The distance in which the particle travels is given by the region between the graph and the X-axis.

The area above the X-axis is the distance traveled in the positive direction Whereas the area below the X-axis is the distance traveled in the negative.

If its distance is positive  = area between t=0 s to t=20 s.  

                                        $=\frac{1}{2} \times 20 \times 5$

                                        $=\frac{1}{2} \times 100$

                                        = 50 m

If its distance is negative = area from t=20 s to t=40 s

                                         $=\frac{1}{2} \times 20 \times 5$

                                         $=\frac{1}{2} \times 100$

                                        = 50 m    

The total distance traveled  = 50 m + 50 m = 100 m.  

Since the distance traveled positively and negatively is equal, the particle returns to its original position, So displacement is zero. Therefore average velocity is zero.