Question

If the kinetic energy of a body is directly proportional to time t, the magnitude of the force acting on the body is :

• A. directly proportional to $\sqrt{t}$
• B. inversely proportional to $\sqrt{t}$
• C. directly proportional to the speed of the body
• D. inversely proportional to the speed of the body

Answer 1

Answer: (B), (D)

inversely proportional to $\sqrt{t}$
inversely proportional to the speed of the body

$\frac{1}{2}m{v}^2=\alpha \left(t\right)$

or

$v\propto \frac{1}{t^2}$

Therefore,

$a=\frac{dv}{dt}\propto \sqrt{t}$

or

$F\propto \frac{1}{\sqrt{t}}\propto \frac{1}{v}$