• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Calculus: Given parabola and vx in terms of x and c, prove constant velocity

  • Thread starter derelictee
  • Start date
Here an AP Physics problem that's really bugging me.
1. Homework Statement

A particle moves along the parabola with equation y = .5x^2

part a) I believe I did this correct.

part b) Suppose that the particle moves with a velocity whose x-component is given by vx = c / (1 + x^2)^.5 Show that the particle's speed is constant.

Below I have images of the question and my attempted work. I think maybe for the first half of my work I was in the right direction; I got y in terms of t, and I was going to find the derivative to show that there is no acceleration, but I couldn't get the equation to equal y, and I ultimately became confused and went off track.


3. The Attempt at a Solution
http://img363.imageshack.us/img363/7313/scanqa9.th.jpg [Broken]http://g.imageshack.us/thpix.php [Broken]
http://img218.imageshack.us/img218/2346/scan0001fu2.th.jpg [Broken]http://g.imageshack.us/thpix.php [Broken]
I know; my work is a mess.
 
Last edited by a moderator:

LowlyPion

Homework Helper
3,079
4
Here an AP Physics problem that's really bugging me.
1. Homework Statement

A particle moves along the parabola with equation y = .5x^2

part a) I believe I did this correct.

part b) Suppose that the particle moves with a velocity whose x-component is given by vx = c / (1 + x^2)^.5 Show that the particle's speed is constant.

Below I have images of the question and my attempted work. I think maybe for the first half of my work I was in the right direction; I got y in terms of t, and I was going to find the derivative to show that there is no acceleration, but I couldn't get the equation to equal y, and I ultimately became confused and went off track.

I know; my work is a mess.
Have you considered that if Vx = c/(1+x2)1/2 that x would be given by the integral?

In this regard isn't the x position as a function of time given by the integral of Vx(t)

[tex] \int \frac{c*dx}{(x^2 + 1)^{1/2}} = c*arcsinh(x) + C = c*arcsinh(x) + c[/tex]

C is c because V=c at x=0
 

Related Threads for: Calculus: Given parabola and vx in terms of x and c, prove constant velocity

Replies
3
Views
27K
Replies
29
Views
651
  • Posted
Replies
2
Views
2K
  • Posted
Replies
1
Views
1K
Replies
1
Views
7K
Replies
1
Views
3K
  • Posted
Replies
0
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top