The K.E. of a body moving along a straight line varies with time as shown in the figure. The force acting on the body is

zero

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independent of velocity

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inversely proportional to velocity

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directly proportional to square of velocity

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Solution

The correct option is C inversely proportional to velocity
Rate of change in kinetic energy = Power = Force * Velocity
$K . E \propto t \Rightarrow K . E = c t$
$\frac{1}{2} m v^{2} = c t \Rightarrow v = \sqrt{\frac{2 c t}{m}} a = \frac{d v}{d t} = \sqrt{\frac{2 c}{m}} \times \frac{1}{2 \sqrt{t}} ∴ F = m a$

$F = m = \sqrt{\frac{c}{2 m t}} = \sqrt{\frac{c}{2 m (K E) / c}} = \frac{c}{m v} ⟹ F \propto 1 / v$
Means force is inversely proportional to velocity.

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The K.E. of a body moving along a straight line varies with time as shown in the figure. The force acting on the body is

The correct option is C inversely proportional to velocityRate of change in kinetic energy = Power = Force * Velocity K.E∝t⇒K.E=ct 12mv2=ct⇒v=√2ctma=dvdt=√2cm×12√t∴ F=ma F=m=√c2mt=√c2m(KE)/c=cmv⟹F∝1/v Means force is inversely proportional to velocity.