# Derive an expression for the velocity of a ball on an incline as a function of the position?

I am trying to derive an expression for the velocity of the ball's center of mass as a function of the positon x. After this, I want to determine the acceleration of the ball's center of mass as it rolls.
I have made a sketch of the situation:
https://ibb.co/cpkLXS
Description: We have a man with the mass...
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I am trying to derive an expression for the velocity of the ball's center of mass as a function of the positon x. After this, I want to determine the acceleration of the ball's center of mass as it rolls.

I have made a sketch of the situation:

https://ibb.co/cpkLXS

Description: We have a man with the mass M=80 kg, who is running at a constant velocity of v = 5 m/s down the incline. The incline has an angle, theta, of 20 degrees measured from horizontal. At time t = 0 s, the man passes a ball. The ball is initially at rest, but it starts to roll (no gliding/slipping) at t = 0 s. The ball is hollow, has a radius R = 20,0 cm and a mass of m = 9,00 kg. We assume that there is no air resistance or friction between the ball and the incline.

I have decided to put the x-axis along the incline with x = 0 at the place where the ball starts to roll from.

I have made a sketch of the situation:

https://ibb.co/cpkLXS

Description: We have a man with the mass M=80 kg, who is running at a constant velocity of v = 5 m/s down the incline. The incline has an angle, theta, of 20 degrees measured from horizontal. At time t = 0 s, the man passes a ball. The ball is initially at rest, but it starts to roll (no gliding/slipping) at t = 0 s. The ball is hollow, has a radius R = 20,0 cm and a mass of m = 9,00 kg. We assume that there is no air resistance or friction between the ball and the incline.

I have decided to put the x-axis along the incline with x = 0 at the place where the ball starts to roll from.

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