# Find acceleration of a particle when given a velocity function in terms of displacement.

Particle B moves such that its velocity $$v\>ms^{-1}$$ is related to its displacement $$s\>$$m, by the equation $$v(s)=arcsin(\sqrt{s})$$. Find the acceleration of particle B when $$s=0.1$$m.

My attempt:

$$\frac{dv}{ds}=\frac{1}{2\sqrt{s(1-s)}}=\frac{1}{2\sqrt{0.1(0.9)}}=\frac{5}{3}$$, but this is not the answer.

• Acceleration is $dv/dt$, not $dv/ds$. – zipirovich Nov 4 '18 at 20:14
• @zipirovich, I agree with you, so how do I proceed from here? – Jane T Nov 4 '18 at 20:35
• Hint: Chain rule. – Robert Israel Nov 4 '18 at 20:40

By the Chain Rule: $$\frac{dv}{dt}=\frac{dv}{ds}\cdot\frac{ds}{dt}=\frac{dv}{ds}\cdot v=\frac{\arcsin\left(\sqrt{s}\right)}{2s\sqrt{s(1-s)}},$$ and you can plug in now.