Question

the velocity of a body depends on the time as v=20+0.1t² show that the body is undergoing non uniform acceleration.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Acceleration}\mathrm{is}\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{change}\mathrm{of}\mathrm{velocity},\mathrm{i}.\mathrm{e}., \\ \mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}} \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \mathrm{v}=20+0.1{\mathrm{t}}^2 \\ \mathrm{a}=\frac{\mathrm{d}}{\mathrm{dt}}\left(20+0.1{\mathrm{t}}^2\right) \\ \mathrm{a}=0+0.1\left(2\mathrm{t}\right) \\ \mathrm{a}=0.2\mathrm{t} \\ \mathrm{which}\mathrm{shows}\mathrm{that}\mathrm{acceleration}\mathrm{depends}\mathrm{on}\mathrm{time}.\mathrm{Hence},\mathrm{it}\mathrm{is}\mathrm{non}-\mathrm{uniform} \\ \mathrm{acceleration}\mathrm{as}\mathrm{it}\mathrm{increases}\mathrm{with}\mathrm{increasing}\mathrm{time}. \end{gathered}$$