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

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

Tardigrade Admin · Accepted Answer

Acceleration, a=2t+5 (dv/dt)=2t+5 dv=(2t+5)dt ...(i) Integrating Eq. (i) both sides within the limits ∫0vdv=∫05(2t+5)dt v=[ (2t2/2)+5t ]05 =[5× 5+5× 5] v=50m/s

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

50 m/s

25 m/s

100 m/s

75 m/s

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

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