# Speed of coin

## 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 travelling 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
Mentor

## 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 travelling 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?

## The Attempt at a Solution

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?

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.

Last edited:
Chestermiller
Mentor
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.

So how would you recommend doing it as a beginner?

Chestermiller
Mentor
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