Parametric Equation Problem

  • Thread starter Feldoh
  • Start date
  • Tags
    Parametric
In summary: It's a transcendental equation and there's no algebra that can help you. You might be able to get close with a numerical analysis, but you'll never be able to solve it exactly.)
  • #1
Feldoh
1,342
3

Homework Statement


A particle moves in the xy-plane so that its position at any time t, 0 =< t =< pi, is given by:
[tex]x(t) = \frac{t^2}{2}-ln(1+t)[/tex]
[tex]y(t) = 3sint[/tex]

-- At that time is the particle on the y-axis on the interval? Find the speed and acceleration vector of the particle at this time.


Homework Equations


None?


The Attempt at a Solution


I'm actually lost -- I believe that when x(t) = 0 it will be on the y-axis but I must be doing the algebra wrong I can't seem to get an exact solution...
 
Physics news on Phys.org
  • #2
You can't solve it exactly algebraically. A well reasoned guess for a value of t such that x(t)=0 will give you the answer though.
 
  • #3
Dick said:
You can't solve it exactly algebraically. A well reasoned guess for a value of t such that x(t)=0 will give you the answer though.

So my method is right up to the point I was at? I should mention I needed to find a t value such that 0 < t < pi, so I don't think 0 is the answer, I should have added that, sorry. Eye-balling the graph it's something like t=1.25 but my teacher claims that it is possible to get an exact solution, but not that you've confirmed it I really don't think there is...

Oh and, velocity is <x'(t), y'(t)> or (x'(t))i+(y'(t))j and acceleration is <x''(t), y''(t)> or (x''(t))i+(y''(t))j
 
  • #4
What's wrong with t=0?
 
  • #5
Dick said:
What's wrong with t=0?

Nothing I just forgot to add that the problem asks for a value of t > 0. I know it works but the problem isn't asking for it I don't think. My mistake I should have clarified:(
 
Last edited:
  • #6
Your post does say t>=0. You've eyeballed the t>0 root correctly. But there's no way you can solve for that one in terms of elementary functions.
 

1. What is a parametric equation?

A parametric equation is a set of equations that express a set of quantities as explicit functions of one or more independent variables, known as parameters. These equations are commonly used in mathematics, physics, and engineering to describe the behavior of a system.

2. How do you solve a parametric equation problem?

To solve a parametric equation problem, you first need to identify the independent variable or parameter and the dependent variable. Then, you can use algebraic techniques such as substitution or elimination to solve for the values of the variables. Graphing the equations can also help visualize the problem and find solutions.

3. What are some real-life applications of parametric equations?

Parametric equations are used in many real-life applications, such as describing the motion of objects in physics, modeling the growth of populations in biology, and designing curves and surfaces in computer graphics. They are also used in engineering for designing and analyzing systems.

4. Can you use parametric equations to solve problems involving circles and ellipses?

Yes, parametric equations can be used to solve problems involving circles and ellipses. In fact, the standard equations for a circle and ellipse are often written in parametric form. This allows for a more flexible and general approach to solving problems involving these shapes.

5. Are parametric equations always unique?

No, parametric equations are not always unique. A system of equations can have multiple parametric solutions, depending on the values of the parameters. In some cases, there may also be infinite solutions or no solutions at all.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
465
  • Calculus and Beyond Homework Help
Replies
5
Views
595
  • Calculus and Beyond Homework Help
Replies
6
Views
474
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
774
  • Calculus and Beyond Homework Help
Replies
2
Views
621
  • Calculus and Beyond Homework Help
Replies
3
Views
515
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
7K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top