Inclined Plane Physics Help

Question

A 1500 kg car starts from rest, and rolls down a frictionless 5.09˚ slope that is 17.5 m long. How much time does it take to reach the bottom? Unit=s

 

This is an example from my book, just different numbers. I was wondering do you go back to kinematic equations to find the time, and if so, how? 

Answer 1

First method

 

The component of acceleration due to gravity down the plane = g * sine(of the angle of slope)

 

= 9.8 sin(5.09) = 9.8 * 0.089 = 0.869 m/s^2

 

Using equations of linear motion

 

U = 0; a = 0.869; x = 17.5 m

 

x =1/2 a*t^2

 

t = (2*x/a)^1/2 = (2*17.5/0.869)^1/2 = 6.36 seconds

 

 

Second method

 

height of plane = 17.5 sine(5.09) - 1.55 m

 

with the absence of friction, PE at top of plane = KE at bottom of plane

 

mgh = 1/2* m*v^2; giving v = (2gh)^1/2 = 5.5 m/s

 

x = t(u + v)/2

 

t = 2*x/(u + v) = 2*17.5/5.5 = 6.36 s