Question

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

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

Answer 1

Answer: (A)

Velocity, $v=\frac{\text{ displacement }}{\text{ time }}=\frac{s}{t}$
Acceleration, $=\frac{s}{t^2}$
Kinetic energy,
$K\cdot E=\frac{1}{2}$ mass $\times$ velocity ${}^2=a{s}^2$
mass $=\frac{2a{s}^2}{s^2/t^2}=2a{t}^2$
Force, $F=$ mass $\times$ acceleration
$=2a{t}^2\frac{s}{t^2}=2as$
Hence, force is $2as$