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 :

directly proportional to t⁴

\(f = kt\)

\(m \int_0^v dv = k\int_0^t t.dt\)

\(mv =\frac{1}{2} kt^2\)

\(v = \frac{k}{2m}t^2\)

KE : \(\frac{1}{2}mv^2 = \frac{1}{2}m.\frac{k^2}{4m^2}.t^4\)

    = \(\frac{k^2}{8m}.t^4\)

\(\Rightarrow KE \propto t^4\)