Math Help - acceleration

1. acceleration

I have done the first part. The second appears to require integrating v. Could I have some help?

2. Re: acceleration

start by taking the derivative on the far right side w/r to s ...

$\frac{d}{ds}\left(\frac{v^2}{2}\right) = v \cdot \frac{dv}{ds} = \frac{ds}{dt} \cdot \frac{dv}{ds} = \frac{dv}{dt} = a$

3. Re: acceleration

Note that

$a=a\cdot\frac{ ds}{ds}= {dv \over dt}\cdot\frac{ ds}{ds}={ds \over dt}\cdot\frac{ dv}{ds}=v\left(\frac{dv}{ds} \right)$