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  4. Displacement-time equation of a particle moving a long x-axis is s = 8 + 3t + 4t2, then find the velocity of particle at t = 5 s.

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Q. Displacement-time equation of a particle moving a long $x$-axis is $s = 8 + 3t + 4t^2$, then find the velocity of particle at $t = 5\, s$.

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Solution:

$s = 8 + 3t +4t^2$
Differentiating with respect to $t$, we get
$\frac{ds}{dt} = 0+3 +8t $
at $t= 5\, sec$
$ \frac{ds}{dt} = v= 3+8\times 5 = 43\, m$