1. Tardigrade
  2. Question
  3. Physics
  4. If the velocity of a particle is given by v=(180-16x)1/2 m/s . then its acceleration will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

J & K CETJ & K CET 2004Motion in a Straight Line

Solution:

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