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

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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}} $