Question

A car starts from rest origin an straight line with an acceleration $\left(a\right)$ given by the relation $a=\frac{25}{(x+2{)}^3}$, where $a$ is in ${\text{m/s}}^2$ and $x$ is in metre. The maximum velocity of the car will be ($x$ is the position of the car)

• A. $2.5\text{m/s}$
• B. $5\text{m/s}$
• C. $10\text{m/s}$
• D. Infinite

Answer 1

The correct option is A $2.5\text{m/s}$

$a=v\frac{dv}{dx}=\frac{25}{(x+2{)}^3},\frac{v^2}{2}=25{[-\frac{1}{2(x+2{)}^2}]}_0^x,v^2=25[\frac{1}{4}-\frac{1}{(x+2{)}^2}]$
$v=\sqrt{25[\frac{1}{4}-\frac{1}{(x+2{)}^2}]},v_{max}=\frac{5}{2}=2.5\text{m/s}$
(at $x=\infty$)
$\therefore$ (a).