Question

Figure (3-E3) Shows the graph of velocity versus time for a particle going along the X-axis. Find (a) the acceleration, (b) the distance travelled in 0 to 10 s and (c) the displacement in 0 to 10 s.
Figure

Answer 1

(a) The acceleration = 0.6 m/s²

(b) The distance = 50 m.

(c) The displacement  = 50 m.

Explanation:

given data in the question  

Velocity at t=0 s is 2 m/s,

velocity at t=10 s is 8 m/s  

(a) To find the acceleration :

                  $acceleration =\frac{\text { Change in velocity }}{\text { time interval }}$

                  $\text {acceleration}=\frac{\Delta v}{t}$

                  $\text {acceleration}=\frac{8-2}{10}$

                  $\text {acceleration}=\frac{6}{10}$

                  acceleration = 0.6 m/s²

(b) To find the distance :

The distance traveled is given between t=0 and t=10 s by the area under the graph

                      $=\frac{1}{2}(2+8) \times 10$      

                      $=\frac{1}{2}(10) \times 10$

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

                      $=50 \mathrm{m}$

(c) To find the displacement :

As the particle travels in one direction, the displacement magnitude along the X-axis is equal to the distance traveled = 50 m.