# The kinetic energy of a body varies directly as the time (t) elapsed. The force acting varies directly as

Q: The kinetic energy of a body varies directly as the time (t) elapsed. The force acting varies directly as

(a) t

(b) √t

(c) 1/√t

(d) 1/t

Ans: (c)
Sol: Kinetic Energy , $\displaystyle K = \frac{1}{2} m v^2$

$\displaystyle K \propto v^2$  …(i)

According to question , $K \propto t$ …(ii)

From (i) & (ii)

$\displaystyle v \propto \sqrt{t} = c \sqrt{t}$

$\displaystyle \frac{dv}{dt} = c \frac{1}{2 \sqrt{t}}$

$\displaystyle a \propto \frac{1}{\sqrt{t}}$

$\displaystyle F \propto \frac{1}{\sqrt{t}}$