First slide

Instantaneous acceleration

Question

A body of mass 2kg travels according to the relation $x (t) = p t + q t^{2} + r t^{3}$ , where $q = 4 {ms}^{- 2}, p = 3 {ms}^{- 1}$
and r = 5 $m s^{- 3}$ . The force acting on the body at t = 2 s is

Moderate

A

136 N
B

134 N
C

158 N
D

68 N

Solution

Given, mass, $m = 2 kg$
$x (t) = p t + q t^{2} + r t^{3}$
Velocity, $v = \frac{d x}{d t} = p + 2 q t + 3 r t^{2}$
Acceleration, $a = \frac{d v}{d t} = 0 + 2 q + 6 r t$
At $t = 2 s, a = 2 q + 6 \times r \times 2 = 2 q + 12 r$
$= 2 \times 4 + 12 \times 5 = 8 + 60 = 68 {ms}^{- 1}$
$Force, F = m a = 2 \times 68 = 136 N$

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