The acceleration of an oscillating sphere is defined by the equation $a=-ks$. Find the value of $k$ such as $v=10\,\frac{cm}{s}$ when $s=0$ and $s=5$ when $v=0$.

The given alternatives in my book are as follows:

$\begin{array}{ll}

1.&15\\

2.&20\\

3.&10\\

4.&4\\

5.&6\\

\end{array}$

What I attempted to do here is to use integration to find the value of $k$.

Since the acceleration measures the rate of change between the speed and time then:

I'm assuming that they are using a weird notation *"s"* for the time.

$\dfrac{d(v(s))}{ds}=-ks$

$v(s)=-k\frac{s^2}{2}+c$

Using the given condition: $v(0)=10$

$10=c$

$v(s)=-k\frac{s^2}{2}+10$

Then it mentions: $v(5)=0$

$0=-k\frac{25}{2}+10$

From this it can be obtained:

$k=\frac{20}{25}=\frac{4}{5}$

However this value doesn't appear within the alternatives. What part did I missunderstood?. Can somebody help me here?. :unsure: