# Speed on an Inclined plane

1. Dec 5, 2009

### abpandanguyen

1. The problem statement, all variables and given/known data

Consider 4 frictionless slides described by the equations

(1) y = sqrt(x), (2) y = x, (3) y = 2x, (4) y = x2. If you start at rest at y = h and slide down to y = 0, which statement regarding your speed v at y = 0 is correct?

2. Relevant equations

(1/2)mv2 = KE
mgh = PE

3. The attempt at a solution
The answer to this question is that all the speeds are equal at y = 0

I know the question asks for speed and that speed is distance over time, so doesn't that mean their speeds should differ taking 1, 2, 3, and 4 into account?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 5, 2009

### kuruman

Speed is "distance over time" only if there no acceleration, i.e. when the object covers equal distances in equal times. I don't know what y = x2 means, but if it describes a slide, there must be acceleration in case (4) also. Try conservaion of mechanical energy and see what that tells you.

3. Dec 5, 2009

### abpandanguyen

o whoops I meant to put that as x^2

I solved for v using conservation of mechanical energy but all my v values came out rather different still. I think I might be doing it wrong...

4. Dec 5, 2009

### kuruman

Can you show what you did and exactly how your v values came out wrong?

5. Dec 5, 2009

### abpandanguyen

here's one example

1.
mgsqrt(x) = (1/2)mv2

sqrt(2g(sqrt(x))) = v

2.
mgx = (1/2)mv2
sqrt(2gx) = v

6. Dec 5, 2009

### kuruman

In all cases the initial kinetic energy is zero and the final potential energy is zero. So the initial potential energy is equal to the final kinetic energy. That's conservation of mechanical energy. Now answer this question, if in all cases the mass starts at height h, what is its initial potential energy?

7. Dec 5, 2009

### abpandanguyen

I think I am getting confused by the
y=sqrt(x), y = x etc.

so having that aside, if they all start from the same height, that means they should all have the same initial potential energy and thus same final kinetic energy and given this, when you write the equations out, they all have the same velocity?

is x representing the horizontal distance here?

8. Dec 5, 2009

### kuruman

Yes, they have the same speed.

Yes, it does.

9. Dec 5, 2009

### abpandanguyen

thank you!
want to help me on my other recent post? >_<