An object moves in such a way that when it has moved a distance s its velocity is $v = \sqrt{s}$ $v=sqrts$ , how do you find its acceleration?

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Answer 1 · 2016-12-15T13:54:39

acceleration = $\frac{1}{2}$ $1/2$

The velocity, $v$ $v$ , is defined as $v = \frac{d s}{d t}$ $v=(ds)/dt$ , and the acceleration, $a$ $a$ is given by $a = \frac{d v}{d t}$ $a=(dv)/dt$

We are told that $v = \sqrt{s}$ $v=sqrt(s)$

$:. (dv)/(ds) = 1/2s^(-1/2)$
$" " = 1/(2sqrt(s))$

So using the chain rule we can write:

$a = (dv)/dt$
$\ \ = (dv)/(ds) * (ds)/dt$
$\ \ = (1/(2sqrt(s))) * v$
$\ \ = (1/(2sqrt(s))) * sqrt(s)$
$\ \ = 1/2$

An object moves in such a way that when it has moved a distance s its velocity is v=sqrtsv=√sv=sqrts, how do you find its acceleration?