Question

A body starts from rest and moves with uniform acceleration for 2s. It then decelerates uniformly for 3s and stops. If deceleration is 4ms2, the acceleration of the body is ________ ms2.

Answer 1

Hi,

$$\begin{gathered} \mathrm{As}\mathrm{the}\mathrm{body}\mathrm{is}\mathrm{starting}\mathrm{from}\mathrm{the}\mathrm{rest}\mathrm{so}\mathrm{its}\mathrm{initial}\mathrm{velocity}\mathrm{will}\mathrm{be}\mathrm{zero}. \\ \mathrm{When}\mathrm{the}\mathrm{body}\mathrm{is}\mathrm{uniformly}\mathrm{accelerating} \\ \mathrm{Acceleration}\mathrm{of}\mathrm{the}\mathrm{body}\left(a\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ \mathrm{a}=\frac{\mathrm{Final}\mathrm{velocity}-\mathrm{Initial}\mathrm{velocity}}{\mathrm{time}} \\ \Rightarrow a=\frac{v-u}{t} \\ \Rightarrow a=\frac{v-0}{2} \\ \Rightarrow v=2a \\ \mathrm{When}\mathrm{the}\mathrm{body}\mathrm{is}\mathrm{decelerating}\mathrm{uniformly}.\mathrm{Then}\mathrm{final}\mathrm{velocity}\mathrm{will}\mathrm{be}\mathrm{zero}.\mathrm{So}, \\ \mathrm{deceleration}=\frac{\mathrm{change}\mathrm{in}\mathrm{velocity}}{\mathrm{time}} \\ \Rightarrow 4=\frac{2a\mathit{-}0}{3}\left(\because u=2a\right) \\ \Rightarrow a=6\mathrm{m}{\mathrm{s}}^{-2} \end{gathered}$$