Question

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

• A. 2.5 $m/s$
• B. 5 $m/s$
• C. 10 $m/s$
• D. Infinite

Answer 1

The correct option is A 2.5 $m/s$

a = $\frac{dv}{dx}$ $\frac{dv}{dx}=\frac{25}{{(x+2)}^3},\frac{v^2}{2}=25\times {[-\frac{1}{2{(x+2)}^2}]}_0^x,v^2=25[\frac{1}{4}-\frac{1}{{(x+2)}^2}]$

v = $\sqrt{25[\frac{1}{4}-\frac{1}{{(x+2)}^2}]}$
$v_{max}=\frac{5}{2}=2.5m/s(atx=\infty )$