Calculating Time for a Ball Rolling Down an Inclined Plane

[Nuha99]

Q: A ball is at rest on an inclined plane. It begins to roll down with an acceleration of 2 m/s^2. How long does it take the ball to roll 50 m?

This is my work:

find time using, s = ut + 1/2 a t^2

t = sqrt(2s/a)

Plug in the s = 50 and a = 2

Am I right?

Thanks a lot.

 

[HallsofIvy]

Where have you used the fact that this is a rolling ball and not a falling mass point? In particular, you have not taken into account the rotational kinetic energy.

 

[Nuha99]

Thanks for your reply.

A falling object accelerates with acceleration of gravity, g. Here the given acceleration, as I understand, is the acceleration of the center of mass (linear acceleration). Even though the ball is rolling, C.M is moving in a straight line along the incline so that we can use the equation of kinematics.

In particular, you have not taken into account the rotational kinetic energy.

Conservation of energy gives me an expression for the final velocity as a function of initial height of the ball above the ground, and will not allow me to find the time of travel.

 

[LowlyPion]

Thanks for your reply.

A falling object accelerates with acceleration of gravity, g. Here the given acceleration, as I understand, is the acceleration of the center of mass (linear acceleration). Even though the ball is rolling, C.M is moving in a straight line along the incline so that we can use the equation of kinematics.

Conservation of energy gives me an expression for the final velocity as a function of initial height of the ball above the ground, and will not allow me to find the time of travel.

That is correct. Your approach looks correct for this problem.
X = 1/2 a t² in this case because you are given its constant acceleration.