The kinetic energy acquired by a mass m in travelling a certain distance d, star

Question

The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to t is

Options:

A . Directly proportional to t2

B . Independent of t

C . Directly proportional to t4

D . Directly proportional to t

Answer: Option C
:
C
f = kt

m \int_{0}^{v}

dv =

k \int_{0}^{t}

tdt
mv = k

t^{2}

v =

\frac{k}{m}

t^{2}

KE =

\frac{1}{2}

v^{2}

\frac{1}{2}

\frac{k^{2}}{m^{2}}

t^{4}

(

\frac{k^{2}}{2 m}

)

t^{4}

α

t^{4}

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