Solving Parametrics: Sketch, Min Value, & Speed/Accel

  • Thread starter saywhaaaat
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In summary, the particle's position at any time t is given by x(t) = ((t squared)/2))-ln(1+t) and y(t) = 3sint. The minimum value of x(t) occurs at t=0 and t=pi, and the position of the particle at this time is (x(t), y(t)). The particle is on the y-axis at t=0 and t=pi, and the speed and acceleration vector at this time can be found by setting the x(t) function to 0.
  • #1
saywhaaaat
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Homework Statement


A particle moves in the xy-plane so that its position at any time t, 0 less than or equal to t, less than or equal to pi, is given by x(t) = ((t squared)/2))-ln(1+t) and y(t) = 3sint

a. sketch
b. At what time t, 0 less than or equal to t, less than or equal to pi, does x(t) attain its minimum value? What is the position (x(t), y(t)) of the particle at this time?
c. At what time t, 0 less than or equal to t, less than or equal to pi, is the particle on the y-axis? Find the speed and the acceleration vector of the particle at this time.



Homework Equations





The Attempt at a Solution



b. t=0, pi

c. set x(t) function to 0?
 
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  • #2
c. Yes.
b. Can you describe how you got this answer?
 
  • #3
Well it seems like you know what to do for the problem but you didn't show us any work for how you got the answer. So we can't help much
 

FAQ: Solving Parametrics: Sketch, Min Value, & Speed/Accel

What is the purpose of solving parametrics?

The purpose of solving parametrics is to find the relationships between various variables in a system and analyze how they change over time. This can help in predicting future values and understanding the behavior of the system.

What is a parametric sketch and how is it used in solving parametrics?

A parametric sketch is a visual representation of a parametric equation. It helps in understanding the shape and behavior of a curve by showing how different variables affect its position and movement. In solving parametrics, parametric sketches are used to find the minimum value of a function and to determine the speed and acceleration of an object.

How do you find the minimum value of a parametric function?

To find the minimum value of a parametric function, you need to first find the derivative of the function with respect to the parameter. Then, set the derivative equal to zero and solve for the parameter value. This value will give the minimum value of the function.

What is speed and acceleration in parametric equations?

In parametric equations, speed is the rate at which the position of an object changes with respect to time. It is given by the magnitude of the velocity vector. Acceleration, on the other hand, is the rate at which the velocity of an object changes with respect to time. It is given by the derivative of velocity with respect to time.

Why is solving parametrics important in the field of science?

Solving parametrics is important in the field of science as it helps in understanding and analyzing the behavior of systems in various fields such as physics, engineering, and economics. It allows scientists to make predictions and develop models to explain real-world phenomena. It also helps in optimizing processes and finding solutions to complex problems.

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