First slide

Instantaneous acceleration

Question

The acceleration ‘a’ in m/s² of a particle is given by $a = 3 t^{2} + 2 t + 2$ where t is the time. If the particle starts out with a velocity u = 2m/s at, t = 0 then the velocity at the end of 2 second is

Moderate

A

12 m/s
B

18 m/s
C

27 m/s
D

36 m/s

Solution

$\begin{array}{l} v = u + \int adt = u + \int (3 t^{2} + 2 t + 2) dt \\ = u + \frac{3 t^{3}}{3} + \frac{2 t^{2}}{2} + 2 t = u + t^{3} + t^{2} + 2 t \end{array}$
$= 2 + 8 + 4 + 4 = 18 m / s$ (As t = 2 sec)

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