A body of mass $10 k g$ carries a braking engine of negligible mass (like a rocket), producing a thrust $|\vec{F}| = k t$ , where $k = 10 N s^{- 1}$ . The body is moving with a uniform speed of $50 m s^{- 1}$ just before the engine is turned on along a smooth horizontal straight road. Assume that the mass remains constant. Then (with braking distance $x_{0}$ and braking time $t_{0}$ )

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the body will come to rest in $t_{0} = 10 s$ after the engine is turned on

the braking distance $x_{0}$ is $125 m$

if, instead of braking engine, an accelerator producing same value of thrust were turned on, then the distance covered during "braking" time $t_{0}$ is $2 x_{0}$ .

the body will come to rest in $t_{0} = 5 s$ after the braking engine is turned on.

answer is A, C.

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Detailed Solution

$- 10 t = 10 a \frac{d v}{d t} = a = - t v = \frac{- t^{2}}{2} + 50 W h e n v = 0, t = 10 s e c$

$S = 50 - \frac{t^{3}}{6} = 500 - \frac{1000}{6} = \frac{1000}{3} m (3) v = 50 + \frac{t^{2}}{2} S = 50 t + \frac{t^{3}}{6} = 500 + \frac{500}{3} = \frac{2000}{3} m$