Question

The kinetic energy of a particle moving along a straight line increases uniformly with respect to the distance travelled by it. The force acting on the particle is ($v$ is the speed of particle at any time)

• A. constant
• B. proportional to $v$
• C. proportional to $v^{2}$
• D. inversely proportional to $v$

Answer 1

Answer: (A)

$KE \propto x$
$\Rightarrow KE = C_{x}$
$\Rightarrow \frac{1}{2} mv^{2} = Cx $
$\frac{1}{2}$ m2v $\frac{dv}{dt} = C \frac{dx}{dt} $
$\Rightarrow $ mv $\frac{dv}{dt} = Cv $
$m \frac{dv}{dt} = C\Rightarrow $ ma $ = C $
$\Rightarrow F = C \to$ constant