Question

the average velocity of a particle moving in a straight line with constant accelerationis 10 m/s. it started with initial velocity 2 m/s. Find acceleration (in m/s²) and time (in second) for which it is possible.

Answer 1

Given,
Initial velocity, u=2 m/s
Average velocity=10 m/s
We know that,
$$\begin{gathered} \mathrm{Average}\mathrm{velocity}\mathrm{for}\mathrm{uniformly}\mathrm{accelerated}\mathrm{motion}, \\ \mathrm{Average}\mathrm{velocity}=\frac{\mathrm{u}+\mathrm{v}}{2}=10 \\ \mathrm{or}\mathrm{v}+\mathrm{u}=20 \\ \mathrm{or}\mathrm{v}+2=20 \\ \mathrm{or}\mathrm{v}=18\mathrm{m}/\mathrm{s} \\ \mathrm{Now}, \\ \mathrm{Using}\mathrm{v}=\mathrm{u}+\mathrm{at} \\ \mathrm{or}\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}=\frac{18-2}{\mathrm{t}}=\frac{16}{\mathrm{t}} \\ \mathrm{Here}\text{'}\mathrm{a}\text{'}\mathrm{can}\mathrm{be}\mathrm{calculated}\mathrm{by}\mathrm{putting}\mathrm{the}\mathrm{values}\mathrm{of}\text{'}\mathrm{t}\text{'} \end{gathered}$$