Solved

# Another Related Rate question

Posted on 2014-10-19
160 Views
A particle p moves on the curve y = x pow(2) + 1 in such a way that dx / dt = 4.  If s is the distance of P from the point ( 0, 6 ), find ds / dt :  ( a ) in general as a function of x and ( b ) when P is at ( 2, 5).

Please explain how to get started with this problem.

This is University calculus I  related rate problem.
0
Question by:naseeam
• 3
• 3
• 2

LVL 32

Accepted Solution

phoffric earned 400 total points
ID: 40390942
To get started with this problem, draw a line from a point (x,y) on the curve to (0,6). Then, s = f(x,y), and you are given that y = g(x).
0

LVL 1

Author Comment

ID: 40391176
What do they mean by particle p moves on the curve y = x pow(2) + 1 in such a way that dx / dt = 4?
0

LVL 84

Expert Comment

ID: 40391186
Solving
dx / dt = 4
we get
x = 4t +C
Given that, can you find y(t)?
0

LVL 32

Assisted Solution

phoffric earned 400 total points
ID: 40391194
>> What do they mean by particle p moves on the curve y = x^2 + 1 in such a way that dx / dt = 4?
You have a parabola and a particle is moving on it in such a way that its speed in the x-direction is always 4 length-units/second.
0

LVL 1

Author Comment

ID: 40391244
dx / dt = 4
we get
x = 4t +C
Given that, can you find y(t)?

I believe this is integration.  Students haven't learned integration in this class yet.
0

LVL 32

Assisted Solution

phoffric earned 400 total points
ID: 40391269
You don't need integration to compute the derivative ds/dt.

I already mentioned that you can determine s = f(x,y).
And you know that the particle p moves on the curve y = x^2 + 1
So, y = g(x).

So, implicitly, s = h(x), right?
And dx/dt = 4 from your OP.

So, now you can take derivative of s --> ds/dt using what rule?
0

LVL 84

Assisted Solution

ozo earned 100 total points
ID: 40391276
If you have x(t) and y(x), can you get y(t)?
From y(t) and x(t) can you get s(t)?
0

LVL 1

Author Closing Comment

ID: 40391903
Great answers!  Not too much help, not too little help.  Perfect balance!
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

### Suggested Solutions

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…