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Instantaneous Velocity

The displacem...

Question

The displacement s of an object is given as a function of time $t$ by the following equation $s = 2 t + 5 t^{2} + 3 t^{3} .$ Calculate the instantaneous velocity of the object at $t = 1 s$

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Solution

Given,

$s = 3 t^{3} 5 t^{2} + 2 t$

So displacement,

Instant velocity, $v = \frac{d s}{d t} \Rightarrow v = \frac{d (3 t^{3} 5 t^{2} + 2 t)}{d t} = 9 t^{2} + 10 t + 2.......1$

If $t = 1 s$ eqtn {1} becomes

$v = 9 + 10 + 2 = 21 m / s$

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