The displacement of a particle is represented by the following equation: s = 3t3 + 7t2 + 5t + 8 where s is in metre and t in second. The acceleration of the particle at t = 1 s is

Question

The displacement of a particle is represented by the following equation: s = 3t3 + 7t2 + 5t + 8 where s is in metre and t in second. The acceleration of the particle at t = 1 s is (A) 14 m/s2 (B) 18 m/s2 (C) 32 m/s2 (D) zero

Tardigrade Admin · Accepted Answer

Displacement s = 3t3 + 7t2 + 5t +8 ; Velocity = (ds/dt) = 9t2 + 14t + 5 Acceleration = (d2s/dt2) = 18t + 14 Acceleration at (t = 1s) = 18 ×1 + 14 =18 + 14 = 32 m/s2

Q. The displacement of a particle is represented by the following equation : $s = 3 t^{3} + 7 t^{2} + 5 t + 8$ where $s$ is in metre and $t$ in second. The acceleration of the particle at $t = 1 s$ is

$14 m / s^{2}$

$18 m / s^{2}$

$32 m / s^{2}$

zero

Displacement
$s = 3 t^{3} + 7 t^{2} + 5 t + 8$ ;
Velocity $= \frac{d s}{d t}$ $= 9 t^{2} + 14 t + 5$
Acceleration $= \frac{d ^{2} s}{d t ^{2}} = 18 t + 14$
Acceleration at $(t = 1 s)$
$= 18 \times 1 + 14 = 18 + 14 = 32 m / s^{2}$

Q. The displacement of a particle is represented by the following equation : s=3t3+7t2+5t+8 where s is in metre and t in second. The acceleration of the particle at t=1s is

14m/s2

18m/s2

32m/s2