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. inversely proportional to $v$
• C. Proportional to $v$
• D. Proportional to $v^2$

Answer 1

The correct option is A Constant

Kinetic energy
$KE\propto x\Rightarrow KE=Cx\Rightarrow \frac{1}{2}m{v}^2=Cx\frac{1}{2}m2v\frac{dv}{dt}=C\frac{dx}{dt}\Rightarrow mv\frac{dv}{dt}=Cvm\frac{dv}{dt}=Cma=C\Rightarrow F=C$
Final answer: (a)