A ball of radius 0.50 m rolls without slipping on a horizontal surface as shown below. Starting from rest at t = 0, the ball moves with constant angular acceleration 6.0 rad/s2. What is the distance, in meters, traveled by the center of the ball from t = 0 to t = 3.0 s?

The pic is simply a ball moving from left to right on a horizontal plane. All information is provided above.

I'd appreciate any explanation, as opposed to just algebra =)

Thank you!

## Answers (1)

t =3; a =6.0 rad/s2; w0=0

v = u+at

w = 0 + 6 * 3 = 18 rad/s

speed = rw = 0.5 * 18 = 9 m/s

u=0; v = 9; t =3

v = u+at

9 = 0 + 3a

a = 3

v^2 = u^2 + 2as

9^2 = 0 + 2

3ss = 13.5 m

answer

traveled by the center of the ball

Reference:my brain (Prof TBT)