Question

A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional toa. t⁽¹÷²⁾b. tc. t⁽³÷²⁾d. t²

Answer 1

a is the acceleration of body
v is the velocity of body after t sec.
initial velocity of body , u = 0
Let mass of body is m

from Newton's 3rd law,
F = ma
a = (F/m)

from formula, v = u + at
v = at => v = (F/m)t .............(1)

now, power = force × velocity

= F × (F/m)t

= F²t/m

for constant acceleration , force always remains constant.
hence, $P\propto t$
so, Power is directly proportional to time.

hence, option (b) is correct.