Help with this question please!?

Question

A car accelerates uniformly from rest and covers a distance of 65 m in 5.7s. If the diameter of the wheel is 40cm.
1. Find angular acceleration of the wheel. Answer in rad/s^2
2. Find the final angular velocity of one of the car's wheels. Answer in rad/s.
3. Find total number of rotation of the wheel.

I left my book at school, and i dont have any of the formulas to help me. Any help would be greatly appreciated. Thank you in advance.

Answer 1

The Average Linear Speed is {total distance / total time taken} = 65/ 5.7 = 11.4 m/s.

Divide this value by the radius of the wheel to get the ‘The Average Angular Speed’.

The Average Angular Speed is = 11.4 / 0.02 = 570 radian per second.

Since the motion is uniform,

The Average Angular Speed = {Initial Angular Speed + Final Angular Speed} / 2

But the Initial Angular Speed is zero.

Therefore, the Final Angular Speed is twice the Average Angular Speed
= 2 x 570
=1140 radian/ second. (The answer for the second question)

Since the Initial Angular Speed is zero,

The Angular acceleration is, “Final Angular Speed/ total time”.
= 1140/5.7 = 200 [radian / second] / second. The answer for the first question)


The number of revolutions is found by “total distance / (pi x diameter of the wheel)” = 65 / pi 0.04 = 517.25 revolutions.

Answer 2

s = s0 + v0t +(1/2)at^2
1.
a = 2*65/(5.7^2) m/s^2
a = rα
α = 2a/d = 4*2*65*100/(40*5.7^2) rad/s^2

2.
ω = 2v/d = (2*65 m)(100 cm/m)/40

3.
C = πd
n = s/C
n = (65 m)(100cm/m)/(40π)