Question

The kinetic energy $ \, K$ of a particle moving in a straight line depends on the distance s as $K=as^{2}$ . The force acting on the particle is

(where $a$ is a constant)

• A. $2as$
• B. $as$
• C. $2a$
• D. $\sqrt{\textit{as}^{2}}$

Answer 1

Answer: (A)

Here kinetic energy $\text{K} = \frac{1}{2} \text{mv}^{2} = \text{a} \text{} \text{s} ^{2}$
∴ mv² = 2as² ...(i)
Differentiating eqn (i) w.r.t. to time t, we get
$2 \text{mv} \frac{\text{dv}}{ \text{dt}} = 4 \text{as} \frac{ \text{ds}}{\text{dt}} = 4 \text{asv} \text{or} \text{m} \frac{\text{dv}}{\text{dt}} = 2 \text{as}$