# A car is moving by gravity force

## Homework Statement

In t=0 a car is free from it's chain and can fall freely through a inclined plane (10 degrees)
rear wheels weight 500 lb each one and have an diameter of eight feet. Front wheel weights 800 lb and have a radius of 2 feet. The body of vehicle weights 9000 lb. Assume that wheels can drift. Obtain a expression for velocity in function of time.

## Homework Equations

Summation of forces = ma
We have inerce forces and gravity force. gravity force exerted on vehicle equals to Mgsin10

## The Attempt at a Solution

inertia force formula is Ia, then I should add the forces.

M*g*sin(10)+Ialpha=Ma
5.591471 ft/s^2+Ialpha/M=a
alpha is angular acceleration.
A condition for simultaneous rotation and translation movement is v=wr
w=v/r
dw/dt= 1/r(dv/dt)
5.591471M+I(1/r) dv/dt=Mdv/dt
and Inertia applies for each rotating element
5.6M+(I1/r1+I2/r2) dv/dt=Mdv/dt
5.6M+(I1/4+I2/2)dv/dt=Mdv/dt

Moment of inertia for a wheel=mr^2/2.
M is the total mass in the system.
5.6M+(mr^2/2+md^2)/4+ (m1r1^2/2+md2^2)/2))dv/dt=Mdv/dt
5.6M+( (8m+md^2)/4+(2m1+md2^2)/2)dv/dt=Mdv/dt
5.6M+( (8000+1000d^2)/4+(1600+800d2^2)/2)dv/dt=Mdv/dt

D are distances from the axis, they are unknown.
I only should put the expression from dv/dt and integrate for get a expression for v in function of t.

I don't know if my solution is right/
In which step I am wrong?