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

Discussion Forum : Work Power And Energy

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

t^{2}

B . Independent of t

C . Directly proportional to

t^{4}

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 = $\frac{1}{2}$ m $v^{2}$ = $\frac{1}{2}$ m $\frac{k^{2}}{m^{2}}$ $t^{4}$ = $($ $\frac{k^{2}}{2 m}$ $)$ $t^{4}$
KE $α$ $t^{4}$

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