Question

If position of an object is changing as $s=7t^3+\frac{t^2}{2}+3$. Then its acceleration at $t=3\text{sec}$ is

• A. $198{\text{m/s}}^2$
• B. $127{\text{m/s}}^2$
• C. $73{\text{m/s}}^2$
• D. $21{\text{m/s}}^2$

Answer 1

The correct option is B $127{\text{m/s}}^2$

$s=7t^3+\frac{t^2}{2}+3$
$v=\frac{ds}{dt}=21t^2+t$
$a=\frac{dv}{dt}=42t+1$
And $a{|}_{\text{at}t=3}=42\left(3\right)+1=127\text{m/s}$