Velocity-time equation of a particle moving in a straight line is, $v = (10 + 2 t + 3 t^{2})$ (SI Units) Find displacement of particle from the mean position at time $t = 1$ second, if it is given that displacement is $20 m$ at time $t = 0$ .

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Solution

The given equation can be written as,
$v = \frac{d s}{d t} = (10 + 2 t + 3 t^{2})$
or $d s = (10 + 2 t + 3 t^{2}) d t$
or $\int_{20}^{s} d s = \int_{0}^{1} (10 + 2 t + 3 t^{2}) d t$
or $s - 20 = {[10 t + t^{2} + t^{3}]}_{0}^{2}$
or $s = 20 + 12 = 32 m$

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Similar questions

v = (10 + 2 t + 3 t^{2})

x = 20 + t^{3} - 12 t

t = 0

x = 3 t^{2} + 2 t + 1

t

t = 3

t = 1 s e c

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