How to Calculate Speed of a Car Rolling Down a Hill

[tommy-d]

Hi there currently I am stuck on a question, A car with a mass of 1.2 tonnes, rolls down a hill which is 600m long and is inclined at an angle of 9 degrees to the horizontal. Ignoring the effects of air resistance and friction and assuming the car to start from rest at the top of the hill calculate:

Its speed as it reaches the bottom of the hill.

Its acceleration down the hill

The time taken for it to reach the bottom of the hill.

The part that I am having the difficulty with is the speed as it reaches the bottom of the hill, I've looked over and over and can't find anything on it. does anyone know a formula for this? or a way to calculate it?

Many thanks Tom

 

[kbaumen]

Welcome to PF!

Velocity changes due to acceleration. What causes the acceleration?

How is acceleration related to some of the given info? Have you studied Newton's laws?

Can you write a velocity equation for this motion?

Please, show your work. Don't be afraid to post wrong answers. It's better if a student submits two pages of nonsense than a blank page.

 

[tommy-d]

the only formula i can get close to for this is ax = T/m- g sin9° i have written this out to be 0/1200-9.81sin(9) = -1.53. this would mean that the speed when the car would be exiting the ramp would be 1.53 m/s but I'm not confident on this answer as it doesn't mention the length of the ramp in the formula. any suggestions?

Many thanks tom

 

[kbaumen]

Can you show me your work? How did you derive this formula?

Try drawing a diagram. Then draw the x-axis (or call it a bob-axis, it doesn't really matter) in the direction of motion. Write down all the forces acting on this car. How is a force connected with acceleration? What is the general equation of motion?

Remember that this case can be simplified to the inclined plane problem (we don't care if it's either Ferrari or an old Volvo). An object with a constant coefficient of friction is sliding down the plane.