Derive the formula: s=ut+1 2 at^2, where the symbols have usual m… - Vidyadip

Question

Derive the formula: $\text{s}=\text{ut}+\frac{1}{2}\text{at}^2,$ where the symbols have usual meanings.

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Answer

Suppose a body has an initial velocity '$u'$ and a uniform acceleration'$ a'$ for time '$t'$ so that its final velocity becomes '$v'$. Let the distance travelled by the body in this time be '$s'$. The distance travelled by a moving body in time '$t'$ can be found out by considering its average velocity. Since the initial velocity of the body is '$u'$ and its final velocity is '$v'$, the average velocity is given by.

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