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 $2m{s}^{-1}$ . When the distance covered by the body is $4m$ , the value of its kinetic energy would be,

• A. $50J$
• B. $40J$
• C. $20J$
• D. $10J$

Answer 1

Answer: (D)

Given:
$m=25kg$
$v_{initial}=2m{s}^{-1}$
So, initial $KE$ of the body, $K{E}_{initial}=\frac{1}{2}m{v}^2=\frac{1}{2}\times 25\times 4=50J$
Here, work done $=$ area of $F-x$ graph,
$\Rightarrow W=areaoftriangle\Rightarrow W=\frac{1}{2}\times base\times height\Rightarrow W=\frac{1}{2}\times 4\times 20\Rightarrow W=40J$
Since, the force is resistive. So, $W=-40J$ .

By work–energy theorem,
$Workdone=changeinkineticenergy$
$W=K{E}_{final}-K{E}_{initial}-40=K{E}_{final}-50K{E}_{final}=10J$