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. $8\,m/s^{2}$
• C. $-8\,m/s^{2}$
• D. $4\,m/s^{2}$

Answer 1

Answer: (C)

$-8\,m/s^{2}$

Answer 2

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