91Ó°ÊÓ

The measurement of change of displacement with respect to time is known as velocity, whereas that of velocity with respect to time is known as acceleration.

The graph for velocity of a motorcycle as a function of time is:

Now, at\(t = 3\,s\), the velocity is constant.

Therefore, acceleration at \(t = 3\,s\) will be zero.

And, from\(t = 3\,s{\rm{ to }}t = 7\,s\), there is change in the velocity.

Therefore, acceleration here will be:

\({a_7} = \frac{{\Delta v}}{{\Delta t}} = \frac{{45 - 20}}{{7 - 3}} = \frac{{25}}{4} = 6.25{\rm{ m/}}{{\rm{s}}^2}\)

Similarly,from\(t = 7\,s{\rm{ to }}t = 11\,s\), there is change in the velocity.

Therefore, acceleration here will be:

\({a_{11}} = \frac{{\Delta v}}{{\Delta t}} = \frac{{0 - 45}}{{11 - 7}} = \frac{{ - 45}}{4} = - 11.25{\rm{ m/}}{{\rm{s}}^2}\)

Hence, the required acceleration are

\({a_3} = 0{\rm{ m/}}{{\rm{s}}^2},\,\,\,{a_7} = 6.25{\rm{ m/}}{{\rm{s}}^2},\,\,{\rm{and }}\,{a_{11}} = - 11.25{\rm{ m/}}{{\rm{s}}^2}\).