Right way to transform $s(t)=1/2g*t^2$ to $v$

Question

My problem is, that I have the following:

$$s(t)=\frac {gt^2}{2}$$ and I need to transform it to get $v$.

Just can't find the right way to do it.

Answer 1

$$v(t)=\frac{\mathrm{d}s(t)}{\mathrm{d}t}=\frac{\mathrm{d}}{\mathrm{d}t} \left (\frac12 g t^2\right ) =\frac12 g\frac{\mathrm{d}}{\mathrm{d}t}(t^2)\;\stackrel{\frac{\mathrm{d}}{\mathrm{d}t} t^n=nt^{n-1}}{=}\; \frac12 \cdot g\cdot 2t=gt$$

Answer 2

$v(t) = \frac{ds(t)}{dt}.$
Can you use it to get $v$?

Answer 3

velocity at any time is defined as the derivative of displacement

So if $v$ is the volcity and $s$ is the displacement then

$$v= \frac {ds}{dt}$$

therefore $$v=\frac g2.2t=gt$$

hope this helped