Question

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

Answer 1

To solve this we are going to use the kinematic equation for final velocity:
`V_(f)=V_(i)+at`
where

`V_(f)` is the final velocity

`V_(i)` is the initial velocity

`a` is the acceleration

`t` is the time

We know for our problem that the the velocity at the beginning of the slope is
`2.0ms^(-1)`, so
`V_(i)=2.0`. We also know that the speed ad the bottom of the slope is
`20ms^(-1)`, so
`V_(f)=20`. We also know that the acceleration is
`6ms^(-2)`, so
`a=6`. Lets replace those values in our formula and solve for
`t`:

`V_(f)=V_(i)+at`

`20=2+6t`

`6t=18`

`t= (18)/(3)`

`t=3` seconds

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