First slide

Instantaneous acceleration

Question

The velocity of a body moving along x direction is related to its displacement as $3 x^{2} - 2 x$ . Acceleration of the body at x=2 m is

Difficult

A

48 $m s^{- 2}$
B

80 m $s^{- 2}$
C

18 $m s^{- 2}$
D

10 $m s^{- 2}$

Solution

$v = 3 x^{2} - 2 x$
$a = \frac{d v}{d t} = \frac{d v}{d x} \frac{d x}{d t} = (6 x - 2) v = 2 (3 x - 1) (3 x^{2} - 2 x)$
putting x=2m $a = 2 (6 - 1) (12 - 4) = 80$ m/ $s^{2}$

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