$s=ut+\frac{1}{2}a{t}^2$

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Prerequisite Materials

$$v=u+at$$

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Derivation

Further, the velocity is the rate of change of displacement so,

$$at+u=\frac{ds}{dt}$$

Integrating,

$$s=\int at+u\mathrm{dt}$$ $$s=\frac{1}{2}a{t}^2+ut+C$$

If we set the inital displacement to zero then this simplifies to:

$$s=\frac{1}{2}a{t}^2+ut$$

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