Question

The kinetic energy of a particle moving in a straight line varies with time $t$ as $k=4t^2$. The force acting on the particle_____ with time.

• A. is increasing
• B. is constant
• C. is decresing
• D. first increases and then decrease

Answer 1

The correct option is A is increasing

Given, kinetic Energy

$K=\frac{1}{2}m{v}^2=4t^2$

Differentiate with respect to time

Rate of change of kinetic energy

$\frac{dk}{dt}=\frac{1}{2}m\left(2v\frac{dv}{dt}\right)=8t$

$\Rightarrow mva=8t$

$\Rightarrow F.v=8t$

From this it is clear

$Force\alpha time$

Hence, force act on particle is increase with time.