First slide

Instantaneous acceleration

Question

A particle moves along a straight line. Its position at any instant is given by $x = 32 t - \frac{8 t^{3}}{4}$ , where x is in metre and t is in second. Find the acceleration of the particle at the instant when particle is at rest.

Moderate

A

$- 16 {ms}^{- 2}$
B

$- 27.6 {ms}^{- 2}$
C

$32 {ms}^{- 2}$
D

$16 {ms}^{- 2}$

Solution

$v = \frac{d x}{d t} = 32 - 6 t^{2}, v = 0 at t = 2.30 s$
$a = \frac{d v}{d t} = - 12 t$
At 2.30 s, a = $- 27.6 {ms}^{- 2}$

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