(a) Derive the formula: s = ut + 1/2 at2, where the symbols have usual meanings.(b) A train starting from stationary position and moving with uniform acceleration attains a speed of 36km per hour in 10 minutes. Find its acceleration.

a). Let a moving body has the initial velocity $u$ and within the time $t$ its velocity becomes $v$ with the acceleration $a$ and let $s$ be the distance covered by the body.


As known acceleration $a=\frac{change\ in\ velocity}{time}$

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

Or $at=v-u$

Or $v=u+at$

We know the average velocity $=\frac{u+v}{2}$

Distance $s=average\ velocity\times time$

Or $s=\frac{u+v}{2}\times t$

Or $s=\frac{u+u+at}{2}\times t$

Or $s=\frac{2u+at}{2}\times t$

Or $s=\frac{2u}{2}\times t+\frac{1}{2}\times at\times t$

Or $s=ut+\frac{1}{2}at^2$


b). Initial velocity of the train $u=o$

Final velocity $v=36\ km/h=36\times\frac{5}{18}=10\ m/s$

Time $t=10\ minutes=10\times60\ sec.= 600sec.$

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

Or $a=\frac{10-0}{600}$

Or $a=\frac{1}{60}\ m/s^2$

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Updated on: 10-Oct-2022

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