The acceleration ' a in m / s 2 of a particle is given by a =3 t 2+2 t +2 where t is the time. If the particle starts out with a velocity u=2 m / s at t =0, then the velocity at the end of v second is

Question

The acceleration ' a in m / s 2 of a particle is given by a =3 t 2+2 t +2 where t is the time. If the particle starts out with a velocity u=2 m / s at t =0, then the velocity at the end of v second is (A) 12 (B) 18 (C) 27 (D) 36

Tardigrade Admin · Accepted Answer

a=3 t2+2 t+2 dv = adt v=(3 t3/3)+(2 t2/2)+2 t v=t3+t2+2 t at t =0, u =2 att =2 v=t3+t2+2 t+2 =8+4+2 × 2+2 =8+4+4+2 =18 m / s

Q. The acceleration ' a in $m / s^{2}$ of a particle is given by $a = 3 t^{2} + 2 t + 2$ where $t$ is the time. If the particle starts out with a velocity $u = 2 m / s$ at $t = 0$ , then the velocity at the end of $v$ second is

12

18

27

36

$a = 3 t^{2} + 2 t + 2$
$d v = a d t$
$v = \frac{3 t ^{3}}{3} + \frac{2 t ^{2}}{2} + 2 t$
$v = t^{3} + t^{2} + 2 t$
at $t = 0, u = 2$
att $= 2$
$v = t^{3} + t^{2} + 2 t + 2$
$= 8 + 4 + 2 \times 2 + 2$
$= 8 + 4 + 4 + 2$
$= 18 m / s$

Q. The acceleration ' a in m/s2 of a particle is given by a=3t2+2t+2 where t is the time. If the particle starts out with a velocity u=2m/s at t=0, then the velocity at the end of v second is

12

18

27

36

a=3t2+2t+2 dv=adt v=33t3​+22t2​+2t v=t3+t2+2t at t=0,u=2 att =2 v=t3+t2+2t+2 =8+4+2×2+2 =8+4+4+2 =18m/s

Q. The acceleration ' a in $m / s^{2}$ of a particle is given by $a = 3 t^{2} + 2 t + 2$ where $t$ is the time. If the particle starts out with a velocity $u = 2 m / s$ at $t = 0$ , then the velocity at the end of $v$ second is

$a = 3 t^{2} + 2 t + 2$
$d v = a d t$
$v = \frac{3 t ^{3}}{3} + \frac{2 t ^{2}}{2} + 2 t$
$v = t^{3} + t^{2} + 2 t$
at $t = 0, u = 2$
att $= 2$
$v = t^{3} + t^{2} + 2 t + 2$
$= 8 + 4 + 2 \times 2 + 2$
$= 8 + 4 + 4 + 2$
$= 18 m / s$