Question

A Gatorade bottle is dropped on a waterslide. It accelerates at 4.0 m/s2 for 9.0s from rest. What is the slide’s length?

Answer 1

With an acceleration of 4.0 m/s², the bottle attains a speed of

(4.0 m/s²) * (9.0 s) = 36 m/s

so that the slide has length ∆x such that

(36 m/s)² - 0² = 2 * (4.0 m/s²) * ∆x

==>  ∆x = 162 m ≈ 160 m

Alternatively, we know the bottle covers a distance ∆x with acceleration a at time t according to

∆x = 1/2 a t²

so that

∆x = 1/2 * (4.0 m/s²) * (9.0 s)² = 162 m ≈ 160 m