how long did it take to reach the bottom of the slope

To solve this we are going to use the kinematic equation for final velocity: [tex]V_{f}=V_{i}+at[/tex]
where
[tex]V_{f}[/tex] is the final velocity
[tex]V_{i}[/tex] is the initial velocity 
[tex]a[/tex] is the acceleration 
[tex]t[/tex] is the time

We know for our problem that the the velocity at the beginning of the slope is  [tex]2.0ms^{-1}[/tex], so [tex]V_{i}=2.0[/tex]. We also know that the speed ad the bottom of the slope is [tex]20ms^{-1}[/tex], so [tex]V_{f}=20[/tex]. We also know that the acceleration is [tex]6ms^{-2}[/tex], so [tex]a=6[/tex]. Lets replace those values in our formula and solve for [tex]t[/tex]:
[tex]V_{f}=V_{i}+at[/tex]
[tex]20=2+6t[/tex]
[tex]6t=18[/tex]
[tex]t= \frac{18}{3} [/tex]
[tex]t=3[/tex] seconds

We can conclude that it takes the roller coaster 3 seconds to reach the bottom of the slope.