Motion of a particle is given by equation s = (3t3+7t2+14t+8) m. The value of acceleration of the particle at t = 1 sec is

Question

Motion of a particle is given by equation s = (3t3+7t2+14t+8) m. The value of acceleration of the particle at t = 1 sec is (A) 10 m/s2 (B) 32 m/s2 (C) 23 m/s2 (D) 16 m/s2

Tardigrade Admin · Accepted Answer

(ds/dt)=9t2+14t+14 ⇒ (d2s/dt2)=18t+14=a at=1 = 18 × 1 + 1 4 = 32 m/s2

Q. Motion of a particle is given by equation $s = (3 t^{3} + 7 t^{2} + 14 t + 8) m .$ The value of acceleration of the particle at $t = 1 sec$ is

$10 m / s^{2}$

$32 m / s^{2}$

$23 m / s^{2}$

$16 m / s^{2}$

$\frac{d s}{d t} = 9 t^{2} + 14 t + 14$
$\Rightarrow \frac{d ^{2} s}{d t ^{2}} = 18 t + 14 = a$
$a_{t = 1} = 18 \times 1 + 14 = 32 m / s^{2}$

Q. Motion of a particle is given by equation s=(3t3+7t2+14t+8)m. The value of acceleration of the particle at t=1 sec is

10m/s2

32m/s2

23m/s2

16m/s2