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

Question

If acceleration of a particle at any time is given by a=2 t+5 calculate the velocity after 5 s, 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

a=2 t+5 or (d v/d t)=2 t+5 or d v=(2 t+5) d t ldots (i) Integrating Eq. (i) on both sides within the limits ∫ limits0v d v=∫ limits05(2 t+5) d t or v=[(2 t2/2)+5 t]05 =[5 × 5+5 × 5]=50 m / s

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

50 m/s

25 m/s

100 m/s

75 m/s

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

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.