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
\(v={\sqrt {2kt\over m}}\space \space {dv\over dt}={\sqrt{k\over2mt}}\)
\(F ={ m.dv\over dt}\)
\(F\propto{1\over \sqrt t}\)