Question

If the velocity of a particle is given by $v=(180-16x{)}^{1/2}m/s$ . then its acceleration will be

• A. zero
• B. $8m/s^2$
• C. $-8m/s^2$
• D. $4m/s^2$

Answer 1

Answer: (C)

$a=\frac{dv}{dt}=\frac{dx}{dt}\frac{dv}{dx}=v\frac{dv}{dx}$
$v=(180-16x{)}^{\frac{1}{2}}$
$v^2=180-16x$
Diff. both sides wrt. $x$,we get:
$2v\frac{dv}{dx}=-16$
$v\frac{dv}{dx}=a=-8m/s^2$