Ball rolling down an inclined plane

[i_need_help]

I have this math problem for school that I need help with

A ball is rolling down an inclined plane. The equation I have is y = .165x^2 + .997x + .845 where y is the distance traveled and x is the time taken

I want to predict the distance it has rolled in 2 days, which I can do

but what sort of assumptions would i have to make?

and what are the strengths and limitations for the model?
for example, a limitation is that when it reaches terminal velocity the model won't work anymore because the model expects the speed to keep increasing

i don't know anything about physics so i need help

 

[cse63146]

Here's what I believe you need:

That equation is if the ball rolls at a constant acceleration. You need assume that it would have constant acceleration, so what would prevent the ball from from going at a constant acceleration?

Not sure about the limitations, though.

 

[Moetasim]

I would first like to commend you for seeking help and taking the time to understand the problem. It shows a great curiosity and dedication to learning.

To answer your question, there are a few assumptions we can make in order to use the given equation to predict the distance traveled by the ball in 2 days.

Firstly, we can assume that the ball is rolling down the inclined plane without any external forces acting on it, such as friction or air resistance. This would ensure that the acceleration remains constant and the equation can accurately predict the distance traveled.

Secondly, we can assume that the ball is rolling in a straight line down the inclined plane, without any changes in direction. This would ensure that the equation, which is based on the concept of motion in a straight line, remains applicable.

Lastly, we can assume that the initial conditions (such as the initial height and velocity of the ball) remain constant throughout the 2 days.

As for the strengths and limitations of the model, you have already mentioned a limitation which is the assumption of constant acceleration. In reality, the acceleration of the ball would change as it reaches terminal velocity.

Another limitation could be the assumption of a perfect inclined plane with no imperfections or irregularities. In real life, there may be small bumps or grooves on the surface of the inclined plane which could affect the motion of the ball.

However, a strength of the model is that it provides a simple and easy-to-use equation to predict the distance traveled by the ball. It also takes into account the effect of time on the distance traveled, which is a key factor in any motion.

In conclusion, while the given equation can provide a good estimate for the distance traveled by the ball, it is important to keep in mind the limitations and assumptions made in the model. Understanding these limitations can help us make more accurate predictions and improve our understanding of the physical world. I hope this helps!