Question

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

• A. $1 \,m / s ^{2}$
• B. $2\, m / s ^{2}$
• C. $5\, m / s ^{2}$
• D. $-5\, m / s ^{2}$

Answer 1

Answer: (D)

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