Question

The graph between the resistive force $ F $ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25kg$ and initial velocity is $ 2 m/s$. When the distance covered by the body is $4m$, its kinetic energy would be:

 $ \text{A}\text{. }10J $
 $ \text{B}\text{. }20J $
 $ \text{C}\text{. }40J $
 $ \text{D}\text{. }50J $

Answer 1

Hint: Work done by a body during its motion can be calculated by finding the area under the Force-displacement graph. Work done is equal to the difference in the initial and final kinetic energy.

Formula used:
$ K.{{E}_{f}}-K.{{E}_{i}}=W $

Complete step-by-step answer:
The principle of work and kinetic energy states that the work done by the sum of all the forces acting on a body is equal to the change in kinetic energy of the body.
$ K.{{E}_{f}}-K.{{E}_{i}}=W $
where $ K.{{E}_{f}} $ is the final kinetic energy of the body, $ K.{{E}_{i}} $ is the initial kinetic energy of the body, and $ W $ is the work done on the body
Initial kinetic energy of the body = $ \dfrac{1}{2}m{{v}^{2}} $
Mass of body is given as $ 25kg $ and the initial velocity is $ 2\dfrac{m}{s} $
We get initial kinetic energy = $ \dfrac{1}{2}\times 25\times {{2}^{2}}=50J $
Work done against the resistive force = area under force-displacement graph
Work done = $ \dfrac{1}{2}\times 4\times 20=40J $
As the work is done against the body, because of resistive force we will take the work done as $ -40J $
Now, Final kinetic energy – Initial kinetic energy = Work done against resistive force
Final kinetic energy = Work done against resistive force + Initial kinetic energy
Final kinetic energy = $ -40+50=10J $
The kinetic energy of the body when it covers the distance of $ 4m $ is $ 10J $ .
Hence, the correct option is A.

Note: Students should not get confused between the positive and negative work done. If the work is done on the body, it is called as positive work done which results in the increase in kinetic energy of the body. If the work is done against the body, it is called as negative work done which results in the decrease in kinetic energy of the body.