What is the acceleration and displacement of a ball rolling up and down a hill?

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Homework Help Overview

The discussion revolves around a problem involving the motion of a ball rolling up and down a hill, with specific focus on its acceleration and displacement over a given time period. The context includes initial and final velocities, as well as the time of travel.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the interpretation of the problem, particularly whether the ball rolled up for the entire 5 seconds or covered a specific distance before rolling down. There are discussions about the effects of gravity on the ball's motion and the implications of the hill's angle on acceleration.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem setup and the implications of the given velocities and time. Some guidance has been offered regarding the effects of gravity and the assumption of a constant angle for the hill, but no consensus has been reached on the specifics of the motion.

Contextual Notes

There are assumptions being made about the starting position of the ball and the nature of its motion, including the potential for initial conditions that are not explicitly stated in the problem. The discussion reflects uncertainty about the parameters affecting the ball's acceleration and displacement.

Carl_M
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A ball rolls at an initial velocity of 4.00 m/s up a hill. 5 seconds later it is rolling down the hill at 6.0 m/s. <---- What does the question mean? Did the ball roll up for 5 seconds and then started rolling down?

Find its acceleration
Find its displacement at 5.0s
 
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Assume it didn't start at the bottom - so it mght be doing 6.0m/s below where it started
 
So did the ball go up 4.00 m/s for 5 secs or go up the hill for 20 meters and then started to roll down at 6 m/s?
 
the ball will be decelarating due to gravity then begins rolling downhill at increasing speed

I think you could assume the hill is at a constant angle so the component of gravity causing the acceleration is constant at g.cos(theta) for whatever theta is...

you know a time and a change in velocity so you should be able to get to what that acceleration is ...
 

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