If acceleration of a particle at any time is a=2t + 5, Calculate the velocity after 5s, if it starts from rest.

If acceleration of a particle at any time is a=2t + 5, Calculate the velocity after 5s, if it starts from rest.

A
50 ${ms}^{- 1}$
B
25 ${ms}^{- 1}$
C
100 ${ms}^{- 1}$
D
75 ${ms}^{- 1}$

Solution:

$a = 2 t + 5 \frac{dv}{dt} = 2 t + 5 \int_{0}^{v} dv = \int_{t = 0}^{t = 5} (2 t + 5) dt v = {(t^{2} + 5 t)}_{t = 0}^{t = 5} v = 50 {ms}^{- 1}$

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