Question

Equation of displacement for any particle is $s=3t^3+7t^2+14t+8m$. Its acceleration at time $t=1sec$ is

• A. $10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$
• B. $16\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$
• C. $25\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$
• D. $32\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Answer 1

The correct option is D

$32\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Step 1. Given data

Equation of displacement is $s=3t^3+7t^2+14t+8m$.

Its acceleration at time is $t=1sec$

Step 2. Calculation part

We know that, acceleration is given by

$$\begin{gathered} a=\frac{d{s}^2}{d{t}^2} \\ =18t+14 \end{gathered}$$

Now substitute $t=1$ in above equation

$a=32\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Hence, the correct option is (D).