Question

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

• A. 50 m/s
• B. 25 m/s
• C. 100 m/s
• D. 75 m/s

Answer 1

Answer: (A)

Acceleration, $ a=2t+5 $
$ \frac{dv}{dt}=2t+5 $ $ dv=(2t+5)dt $ ...(i)
Integrating Eq. (i) both sides within the limits
$ \int_{0}^{v}{dv}=\int_{0}^{5}{(2t+5)}dt $
$ v=\left[ \frac{2{{t}^{2}}}{2}+5t \right]_{0}^{5} $
$ =[5\times 5+5\times 5] $
$ v=50m/s $