Question

The kinetic energy of a body moving along a straight line varies with time as shown in figure. The force, acting on the body:

• A. Zero
• B. constant
• C. directly proportional to velocity
• D. inversely proportional to velocity

Answer 1

The correct option is D inversely proportional to velocity

$K.E\propto t$
$\frac{1}{2}m{v}^2\propto t$
$\frac{1}{2}m{v}^2=Kt$
Differentiating w.r.t time, we get
$\frac{m}{2}2v\frac{dv}{dt}=K$
$\frac{dv}{dt}=\frac{k}{mv}\dots \dots \left(i\right)$
We know that
$F=ma$
$F=m\frac{dv}{dt}$
$F=m\times \frac{K}{mv}\text{F}rom\dots \left(i\right)$
$F=\frac{K}{V}$
$\Rightarrow F\propto \frac{1}{V}$
Final anwer:$\left(d\right).$