Question

A particle moves in a straight line according to the law X=4a[t + Asin(t/a)] where X is its position in meters t in sec and a is some constant then velocity is zero at

Answer 1

Answer:

The velocity is zero when $t=a\:\pi$

Explanation:

Formula used:

$cos^{-1}(-x)=\pi-cos^{-1}x$

Given:

Distance, $x=4a[t+a\:sin(\frac{t}{a})]$

$Velocity=\frac{dx}{dt}$

$Velocity=\frac{d(4a[t+a\:sin(\frac{t}{a})])}{dt}$

$Velocity=4a\frac{d[t+a\:sin(\frac{t}{a})]}{dt}$

$Velocity=4a[1+a\:cos(\frac{t}{a})\frac{1}{a}]$

$Velocity=4a[1+cos(\frac{t}{a})]$

Now,

Velocity = 0

$4a[1+cos(\frac{t}{a})]=0$

$1+cos(\frac{t}{a})=0$

$cos(\frac{t}{a})=-1$

$\frac{t}{a}=cos^{-1}(-1)$

$\frac{t}{a}=\pi-cos^{-1}(1)$

$\frac{t}{a}=\pi-0$

$\frac{t}{a}=\pi$

$t=a\:\pi$

Answer 2

Answer:

Explanation:

Allen module 02