A vehicle is accelerating on a straight road . Its velocity at any instant is $30 k m h^{- 1}$ , after $2 s$ ,it is $33.6 k m h^{- 1}$ and after further $2 s$ it is $37.2 k m h^{- 1}$ .find the acceleration of vehicle in $m s^{- 2}$ . Is the acceleration uniform ?

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Solution

Given velocity $v_{1} = 30 k m / h = 8.33 m / s$
velocity $v_{2} = 33.6 k m / h = 9.33 m / s$
velocity $v_{3} = 37.2 k m / h = 10.33 m / s$
Time interval between $v_{1}$ and $v_{2}$ = 2s and $v_{2}$ and $v_{3}$ =2 s
Now acceleration $a_{12} = \frac{9.33 - 8.33}{2} = 0.5 m / s^{2}$
similarly acceleration $a_{123} = \frac{10.33 - 9.33}{2} = 0.5 m / s^{2}$
Now the net acceleration $a_{12} = \frac{10.33 - 8.33}{4} = 0.5 m / s^{2}$
Yes the acceleration is uniform.

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