A car traveling at 31 m/s runs out of gas while traveling up a 7.0 ∘ slope. How far will it coast before starting to roll back down? I tried using a=g in a kinematic equation but my homework hint said my "a" value is incorrect.

Hi there!

On an incline, the acceleration due to gravity is: (g = 9.81 m/s²)

a = gsinФ ≈ 1.196 m/s²

We can use the following kinematic equation to solve:

vf² = vi² + 2ad

Since the car will start to roll back when v = 0 m/s, we can write that vf = 0.

0 = vi² + 2ad

Plug in values:

0 = 31² + 2(-1.196)(d)

Rearrange for d:

31²/(2.392) = d

d = 401.756 m

answer; equivalent to a one(1) horsepower motor;