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)

$KE\propto x$
$\Rightarrow KE=C_x$
$\Rightarrow \frac{1}{2}m{v}^2=Cx$
$\frac{1}{2}$ 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