Question

If the velocity of a car is given by $V=(150-10x{)}^{1/2}m/s$. If car retards their motion by applying brakes then what will be the acceleration?

• A. $1m/s^2$
• B. $2m/s^2$
• C. $5m/s^2$
• D. $-5m/s^2$

Answer 1

Answer: (D)

$v=(150-10x{)}^{1/2}\Rightarrow \frac{dv}{dt}=\frac{d(150-10x{)}^{1/2}}{dt}\times \frac{dx}{dx}$
$\frac{dv}{dt}=\frac{d(150-10x{)}^{1/2}}{dx}\times \frac{dx}{dt}\Rightarrow a=\frac{d(150-10x{)}^{1/2}}{dx}v$
$a=\frac{1}{2}\times (150-10x{)}^{-1/2}(-10)\times (150-10x{)}^{1/2}$
$a=-5m/s^2$