Question

The displacement of the particle is given by $x=3t^3+6t^2+2t+5$ in $\text{m}$. The instantaneous speed of the particle at $4\text{sec}$ is

• A. $194\text{m/s}$
• B. $180\text{m/s}$
• C. $200\text{m/s}$
• D. $156\text{m/s}$

Answer 1

The correct option is A $194\text{m/s}$

As we know that the instantaneous speed of the particle is given by
$\frac{dx}{dt}=\frac{d(3t^3+6t^2+2t+5)}{dt}$
$\Rightarrow v=9t^2+12t+2$
So, $v{|}_{@\text{t=4 sec}}=9\times 4^2+12\times 4+2=194\text{m/s}$