Consider the following statements $A$ and $B$ identify the correct answer given below : (A) A body initially…
Consider the following statements $A$ and $B$ identify the correct answer given below :
(A) A body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time
(B) When a body is at rest, it must be in equilibrium.
$A$ and $B$ are correct
$A$ and $B$ are wrong
$A$ is correct and $B$ is wrong
$A$ is wrong and $B$ is correct
Solution
$\mathrm{KE}=\frac{1}{2} m v^2=\frac{1}{2} m(a t)^2=\frac{1}{2} m a^2 t^2$
Rate of change of KE,
$\frac{d K}{d t}=\frac{d}{d t}\left(\frac{1}{2} m a^2 t^2\right)=m a^2 t$
$\therefore \quad \frac{d K}{d t} \propto t$
So, statement $A$ is correct.
When the body is at rest, then it may be or may not be in equilibrium, so statement $B$ is wrong.