Question

A particle moves along a straight line such that its displacement at any time t is given by S = 4t^3 +3t^2 + 6t + 8 . Find the acceleration of the particle at t=2s.

Answer 1

Given ,

The displacement of particle at any time t is

• S = 4t³ +3t² + 6t + 8

We know that ,

$\large \boxed{ \sf{Instanteous \: acceleration \: (a) = \frac{ {d}^{2} S}{dt} }}$

Thus ,

$\sf \mapsto a = 24t + 6$

Put t = 2 , we get

$\sf \mapsto a = 24 \times 2 + 6 \\ \\ \sf \mapsto a =54 \: \: m {s}^{ - 2}$

$\sf \therefore{ \underline{The \: acceleration \: of \: the \: particle \: at \: 2 \: sec \: is \: 54 \: </p><p>m {s}^{ - 2} }}$