(a) Derive the formula : $v = u + at$, where the symbols have usual meanings.
(b) A bus was moving with a speed of $54\ km/h$. On applying brakes it stopped in $8\ seconds$. Calculate the acceleration.

(a). If a body is moving with an initial velocity $u$ and within time $t$ its velocity becomes $v$, then 

Its acceleration $a=\frac{Final\ velocity-Initial\ velocity}{time}$

Or $a=\frac{v-u}{t}$

Or $at=v-u$

Or $v=u+at$

(b). Here, the initial velocity $u=54\ km/h$

Final velocity $v=0$

Time $t=8\ seconds$

Therefore, acceleration $a=\frac{v-u}{t}$

Or $a=\frac{0-54}{8}$

Or $a=-6.75\ m/s^2$     [Here -ve sign indicates retardation]

Therefore, acceleration is $-6.75\ m/s^2$.

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Updated on: 10-Oct-2022

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