What is the algebraic expression for the magnitude α of the angular acceleration of the dragster's wheels? Exp

Question

A dragster starts from rest and accelerates down the track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 374 m, the angular speed of the wheels is 276 rad/s.
What is the algebraic expression for the magnitude α of the angular acceleration of the dragster's wheels? Express your answer in terms of the dragster's initial and final linear speeds, v0 and v, the distance x it travels, and the radius r of a wheel.

Answer 1

w = angular acceleration
a = wr

x = v0t + (1/2)a t^2
x = v0t + (1/2)wr t^2

w (r t^2) = 2(x - v0t)
w(r t^2) + 2v0t = 2x

v = v0 + wrt
t = (v - v0)/wr

(v - v0)^2/wr + 2v0(v - v0)/wr = 2x
w = (1/(2xr))((v - v0)^2 + 2v0(v - v0))
w = (1/(2xr))(v - v0)( v - v0 + 2v0)
w = (1/(2xr))(v - v0)(v + v0)

Answer 2

I'll just use W, p, V, g, a, F and m a) W=mg=pVg b) ma = F - W so a=(F - W)/m