Question

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

• A. $14 m/s^2$
• B. $18 m/s^2$
• C. $32 m/s^2$
• D. zero

Answer 1

Answer: (C)

Displacement
$s = 3t^{3} + 7t^{2} + 5t +8 $ ;
Velocity $= \frac{ds}{dt}$ $= 9t^{2} + 14t + 5$
Acceleration $= \frac{d^{2}s}{dt^{2}} = 18t + 14 $
Acceleration at $\left(t = 1s\right)$
$= 18 \times1 + 14 =18 + 14 = 32 m/s^{2} $