Motion in Plane: Find Equations, Velocity & Acceleration Vectors

In summary, the task is to find an equation in x and y that represents the path of a particle in the xy plane at time t, given the position function r(t)=(cos2t)i+(3sin2t)j and a specific value of t. The solution involves finding the equations x=cos2t and y=3sin2t, and adding them to get a familiar equation.
  • #1
jdawg
367
2

Homework Statement



r(t) is the position of a particle in the xy plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at the given value of t.

r(t)=(cos2t)i+(3sin2t)j, t=0

Homework Equations





The Attempt at a Solution



x=cos2t y=3sin2t
x2=cos22t y2/9=sin22t

I'm not sure if I'm on the right track with this! Can someone please give me a push in the right direction?
 
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  • #2
jdawg said:

Homework Statement



r(t) is the position of a particle in the xy plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at the given value of t.

r(t)=(cos2t)i+(3sin2t)j, t=0

Homework Equations





The Attempt at a Solution



x=cos2t y=3sin2t
x2=cos22t y2/9=sin22t

I'm not sure if I'm on the right track with this! Can someone please give me a push in the right direction?

Looks good so far. What do you get if you add those last two equations? Do you recognize it?
 
  • #3
Ohhh thanks, figured it out! :)
 

FAQ: Motion in Plane: Find Equations, Velocity & Acceleration Vectors

What is motion in plane?

Motion in plane refers to the movement of an object in a two-dimensional space, where the object can move in any direction within a specific plane.

How do you find the equations for motion in plane?

The equations for motion in plane can be found by using the principles of kinematics, which involve position, velocity, and acceleration. These equations include the position equation x = x0 + v0t + 0.5at2, the velocity equation v = v0 + at, and the acceleration equation a = (v - v0)/t.

What are velocity and acceleration vectors?

Velocity and acceleration vectors are mathematical representations of the speed and direction of an object's motion. Velocity is a vector that shows the rate of change of an object's position, while acceleration is a vector that shows the rate of change of an object's velocity.

How do you calculate velocity and acceleration vectors?

Velocity and acceleration vectors can be calculated using the equations for motion in plane. The velocity vector is equal to the first derivative of the position vector, while the acceleration vector is equal to the second derivative of the position vector.

What is the significance of velocity and acceleration vectors?

Velocity and acceleration vectors are important in understanding an object's motion in plane because they provide information about the object's speed and direction. They can also be used to predict an object's future position and motion.

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