**At time t = 0s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time ‘t’, the net force acting on it must be proportional to **

(a) \(\sqrt{t}\)

(b) constant

(c) t

(d) \(\frac{1}{\sqrt{t}}\)

**The correct option is d) \(\frac{1}{\sqrt{t}}
\)**

Linear dependency with initial Kinetic Energy as zero is given as KE = kt, where k is the proportionality constant.

Kinetic energy can be written as KE= 1/2 mv^{2 }so we can write

1/2 mv^{2 }= kt

\(v={\sqrt {2kt\over m}}\space \space {dv\over dt}={\sqrt{k\over2mt}}\)

\(F ={ m.dv\over dt}\)

\(F\propto{1\over \sqrt t}\)