First slide

Instantaneous acceleration

Question

A particle is moving along a straight line with an acceleration a = 3t² m/s² where ‘t’ is time in second. Initial velocity of the particle is zero. Then the displacement of the particle at t = 2 sec is

Moderate

A
4 m
B
8 m
C

12 m
D
16 m

Solution

$\frac{d v}{d t} = 3 t^{2} \Rightarrow \int_{0}^{v} d v = \int_{0}^{t} 3 t^{2} d t \Rightarrow v = t^{3} T h e r e f o r e \frac{d x}{d t} = v = t^{3} \Rightarrow \int_{0}^{x} d x = \int_{0}^{2} t^{3} d t \Rightarrow x = 4 m .$

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