Speedbump problem and center of velocity

[Susanne217]

Homework Statement

if a speedbump on a level road has the mathematical equation

$$y = h/2 \cdot (1+cos(\pi \cdot x/b))$$

where B is the length of the road covered by the bump.

If a car starts a point G just before the bump at a speed v then supposedly

the equation of the entire journey is

$$y_G = 1/2 \cdot h/2 \cdot (1+cos(\pi \cdot x/b))$$

What I don't get how do they arrive at that

$$y_G = 1/2 \dot y$$

I am told its something with speed of center?

What can I read more about that?

 

[jbsteele]

Homework Equations y = h/2 \cdot (1+cos(\pi \cdot x/b)) The Attempt at a Solution I'm really stuck here, I can't figure out how the equation was arrived at