Question

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

• A. $20\text{m/s}$
• B. $30\text{m/s}$
• C. $24\text{m/s}$
• D. $36\text{m/s}$

Answer 1

The correct option is B $30\text{m/s}$

As we know that the instantaneous speed of the particle is given by
$\frac{dx}{dt}=\frac{d(2t^2+6t+2)}{dt}$
$\Rightarrow v=4t+6$
So, $v{|}_{@\text{t=6 sec}}=4\times 6+6=30\text{m/s}$