Question

An object is at $2\text{m}$ at $t=0\text{sec}$. Its velocity is given by $v=2t+7$, its position at $t=5\text{sec}$ is

• A. $52\text{m}$
• B. $62\text{m}$
• C. $65\text{m}$
• D. $55\text{m}$

Answer 1

The correct option is B $62\text{m}$

$v=\frac{ds}{dt}=2t+7$
$\int ds=\int (2t+7)dt$
$s=2\frac{t^2}{2}+7t+c$
object is at $2m$ at $t=0\text{sec}$

Given $s{|}_{t=0}=(0{)}^2+7(0)+c=2$
$\Rightarrow c=2$
Now, $s{|}_{t=5}=(5{)}^2+7(5)+2$
$=25+35+2$
$=62m$