Solving for Speed on a Ramp: The Coin's Journey

[eddybob123]

Homework Statement

A coin slides down a ramp angled at 30∘ with respect to the horizontal. If the coin starts from rest, what is its speed in m/s after sliding 1 m?

Homework Equations

The acceleration of an object on a ramp is a=mg*sin(x), where g=9.8 m/s^2 and x is the angle.

The Attempt at a Solution

I know that the acceleration of the coin is 4.9 m/s^2. that means that in the first second it will be traveling at 4.9 m/s, the second second will be 9.8 m/s, then third second 14.7 m/s, etc. However I don't know how to calculate the speed when the time is not an integer. For example, what is the speed of the coin after 2.3 seconds?

 

[Chestermiller]

Homework Statement

A coin slides down a ramp angled at 30∘ with respect to the horizontal. If the coin starts from rest, what is its speed in m/s after sliding 1 m?

Homework Equations

The acceleration of an object on a ramp is a=mg*sin(x), where g=9.8 m/s^2 and x is the angle.

The Attempt at a Solution

I know that the acceleration of the coin is 4.9 m/s^2. that means that in the first second it will be traveling at 4.9 m/s, the second second will be 9.8 m/s, then third second 14.7 m/s, etc. However I don't know how to calculate the speed when the time is not an integer. For example, what is the speed of the coin after 2.3 seconds?

See if the equation v = 4.9 t is consistent with your calculations. What if t is not an integer? Can the equation still be used?

 

[eddybob123]

So what you're saying is that the speed of the object is equal to gt, where g is the acceleration and t is the time displacement. Hmmm... makes sense; the units agree and everything. Why didn't I think of that before?
So how do I know when the coin has slid 1 meter? Seems like a calculus problem upon inspection.

 

[Chestermiller]

So what you're saying is that the speed of the object is equal to gt, where g is the acceleration and t is the time displacement. Hmmm... makes sense; the units agree and everything. Why didn't I think of that before?
So how do I know when the coin has slid 1 meter? Seems like a calculus problem upon inspection.

It is a calculus problem.

 

[eddybob123]

So how would you recommend doing it as a beginner?

 

[Chestermiller]

So how would you recommend doing it as a beginner?

From your profile, I see your favorite area is calculus. If you don't want to use calculus, I guess you can use the formulas:

v = v₀+at

d = d₀+v₀t+at²/2

 

[PhanthomJay]

By now, you should have become familiar with the kinematic equations for uniform acceleration. You already solved for the acceleration, you are given the distance, it starts from rest, and you want to find its speed after traveling that distance. See

https://www.physicsforums.com/showpost.php?p=905663&postcount=2

For the record, you responded

So what you're saying is that the speed of the object is equal to gt, where g is the acceleration and t is the time displacement.

You mean to say v = at, not v = gt.