The acceleration a of the body starting from rest varies with time following the equation a =8 t +5 . The velocity of the body at time t=2 sec will be:

Question

The acceleration a of the body starting from rest varies with time following the equation a =8 t +5 . The velocity of the body at time t=2 sec will be: (A) 22 m / s (B) 26 m / s (C) 28 m / s (D) 30 m / s

Tardigrade Admin · Accepted Answer

a=8 t+5 ⇒ (d v/d t)=8 t+5 ⇒ d v=(8 t+5) d t ∫0v d v=∫0t(8 t+5) d t ⇒ v=(8 t2/2)+5 t v=4 t2+5 t=4 × 4+10=16+10=26 m / s

Q. The acceleration $a$ of the body starting from rest varies with time following the equation $a = 8 t + 5.$ The velocity of the body at time $t = 2$ sec will be:

22 m / s

26 m / s

28 m / s

30 m / s

$a = 8 t + 5 \Rightarrow \frac{d v}{d t} = 8 t + 5 \Rightarrow d v = (8 t + 5) d t$
$\int_{0}^{v} d v = \int_{0}^{t} (8 t + 5) d t \Rightarrow v = \frac{8 t ^{2}}{2} + 5 t$
$v = 4 t^{2} + 5 t = 4 \times 4 + 10 = 16 + 10 = 26 m / s$

Q. The acceleration a of the body starting from rest varies with time following the equation a=8t+5. The velocity of the body at time t=2 sec will be: