Question

A particle starts from rest and moves with acceleration a which varies with time t as a =kt where k is constant .the displacement s of the particle at time t will be

Answer 1

Dear student
acceleration of particle is not constant but varies with time so
$$\begin{gathered} a=\frac{dv}{dt}=kt \\ {\int }_0^{v}dv={\int }_0^{t}ktdt \\ v=\frac{k{t}^2}{2} \\ \frac{dx}{dt}=\frac{k{t}^2}{2} \\ {\int }_0^{x}dx={\int }_0^t\frac{k{t}^2}{2}dt \\ x=\frac{k{t}^3}{6} \end{gathered}$$