First slide

Instantaneous acceleration

Question

A particle is initially at rest at the origin. It starts moving along positive x-axis with acceleration a = 2t m/s2 where t is time in second. Then velocity of the particle at t = 4 second is

Moderate

A
24 m/s
B
4 m/s
C
8 m/s
D
16 m/s

Solution

$\frac{d v}{d t} = a = 2 t \Rightarrow \int_{0}^{v} d v = \int_{0}^{4} 2 t d t \Rightarrow v = 16 m / s$

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