Question

At the moment $t=0$ particle leaves origin and moves in the positive direction of $x$-axis. Its velocity as a function of time is given as $v=(5-t)\text{m/s}$. $x$-coordinate of particle at $t=2\text{s}$ is

• A. $8\text{m}$
• B. $6\text{m}$
• C. $10\text{m}$
• D. $12\text{m}$

Answer 1

The correct option is A $8\text{m}$

$v=\frac{dx}{dt}=(5-t)\Rightarrow {\int }_0^{x}dx={\int }_0^2(5-t)dt$
$x=[5t-\frac{t^2}{2}{]}_0^2\Rightarrow x=5\times 2-\frac{2^2}{2}=8\text{m}$