Q: A body of mass m at rest is subjected to a constant force F for time t. The kinetic energy at time t is given by

(a) F^{2}t^{2} /2m

(b) F^{2}t^{2} /3m

(c) 2 F^{2}t^{2}/m

(d) F^{2}t^{2}/m

Ans: (a)

Solution: Acceleration , a = F/m

Applying , v = u + a t

$\displaystyle v = 0 + \frac{F}{m} t $

$\displaystyle v = \frac{F}{m} t $

Kinetic Energy , $\displaystyle K = \frac{1}{2} m v^2 $

$\displaystyle K = \frac{1}{2} m (\frac{F}{m} t)^2 $

$\displaystyle K = \frac{F^2 t^2}{2 m} $