The acceleration ‘a’ (in ms-2)of a body, starting from rest varies with time t (in s) following the equation a = 3t + 4 The velocity of the body at time t = 2s will be

Question

The acceleration ‘a’ (in ms-2)of a body, starting from rest varies with time t (in s) following the equation a = 3t + 4 The velocity of the body at time t = 2s will be (A) 10 ms-1 (B) 18 ms-1 (C) 14 ms-1 (D) 26 ms-1

Tardigrade Admin · Accepted Answer

Given a=3 t+4 ⇒ (d v/d t)=3 t+4 ∴ ∫ limits0v d v=∫ limits0t(3 t+4) d t ⇒ v=(3/2) t2+4 t at t=2 s v =(3/2)(2)62 + 4(2) = 14 ms-1

Q. The acceleration ‘a’ $(in m s^{- 2})$ of a body, starting from rest varies with time $t$ (in $s$ ) following the equation $a = 3 t + 4$ The velocity of the body at time $t = 2 s$ will be

$10 m s^{- 1}$

$18 m s^{- 1}$

$14 m s^{- 1}$

$26 m s^{- 1}$

Given $a = 3 t + 4$
$\Rightarrow \frac{d v}{d t} = 3 t + 4$
$∴ 0 \int v d v = 0 \int t (3 t + 4) d t$
$\Rightarrow v = \frac{3}{2} t^{2} + 4 t$
at $t = 2 s$
$v = \frac{3}{2} (2) 62 + 4 (2)$
$= 14 m s^{- 1}$

Q. The acceleration ‘a’ (inms−2)of a body, starting from rest varies with time t (in s) following the equation a=3t+4 The velocity of the body at time t=2s will be

10ms−1

18ms−1

14ms−1

26ms−1