Solve Parametric Particle Homework: Find Time, Speed at (3,1)

In summary, the conversation discusses a particle's position along a curve given by a vector equation and the unknown force that keeps it on the trajectory. The question asks at what value of t the force must cease for the particle to pass through a specific point and when it will arrive at that point with what speed. The person has attempted to solve the problem using the slope and point of the tangent line, but has encountered issues with extraneous solutions. However, they have since solved the problem and no longer need assistance.
  • #1
turdferguson
312
0

Homework Statement


Consider a particle along a curve C and whose position is given by the vector:
s(t) = < sqrt(t2), t3 - 3t >

Last part of the question:
There is an unknown force that is keeping this particle on trajectory C. At what value of t must the force cease in order for the particle to pass through the point (3,1)?
When will it arrive at this point and with what speed?

The Attempt at a Solution


Ive tried setting the slope of (3,1) and the point (xt, yt) to equal dy/dx. But I keep getting a value of t that places the point (3,1) on the tangent line behind the particles path. The particle reaches (3,1) at a time before it even gets to (xt, yt) on the curve.

t3-3t-3 / abs(t)-1 = (3t2 -3)t/abs(t)

Is there anything wrong with the setup? Why do I keep getting an extraneous solution when letting t be >0 and when letting t be <0?
 
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  • #2
Nevermind, I got it. This thread can be deleted
 

FAQ: Solve Parametric Particle Homework: Find Time, Speed at (3,1)

How do I solve parametric particle homework?

To solve parametric particle homework, you will need to use the parametric equations given in the problem. These equations represent the position of the particle at a given time. You will also need to use calculus to find the velocity and acceleration of the particle. Once you have the velocity and acceleration, you can use them to find the time and speed at a specific point, such as (3,1).

What is the importance of solving parametric particle problems?

Solving parametric particle problems is important in understanding the motion of objects in real-world situations. It allows us to analyze and predict the position, velocity, and acceleration of a particle at any given time. This is useful in fields such as physics, engineering, and astronomy.

What is the meaning of (3,1) in a parametric particle problem?

In a parametric particle problem, (3,1) represents a specific point in the x-y coordinate system. It could be the initial position of the particle or a point at a certain time. To find the time and speed at this point, you will need to plug in the values of x=3 and y=1 into the parametric equations given in the problem.

How do I find the time and speed at (3,1) in a parametric particle problem?

To find the time and speed at (3,1), you will first need to find the velocity and acceleration of the particle using the given parametric equations. Once you have these values, you can plug them into the equations for time and speed. The time at (3,1) can be found by setting x=3 and solving for t, while the speed at (3,1) can be found by using the equation v=√(vx^2+vy^2) and plugging in the values of vx and vy at (3,1).

What are some tips for solving parametric particle problems efficiently?

Here are some tips for solving parametric particle problems efficiently:

  • Make sure to carefully read and understand the given parametric equations.
  • Use calculus to find the velocity and acceleration of the particle.
  • Plug in the values of x and y at the given point to find the time and speed.
  • Check your calculations and make sure they make sense in the context of the problem.
  • Practice solving different types of parametric particle problems to improve your skills.

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