# At time t = 0s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time ‘t’,

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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) $$\frac{1}{\sqrt{t}}$$

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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 mvso we can write

1/2 mv= kt

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

$$F ={ m.dv\over dt}$$

$$F\propto{1\over \sqrt t}$$
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