# Finding the expression for the x-component of velocity (vectors?)

• ashhlyn
In summary, the problem asks for the expression of the x-component of the velocity of a particle with position vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j, where c and d are positive constants. The solution involves deriving the velocity vector and setting the y-component to zero to find the times when the particle is moving in the x-direction. Plugging those times back into the x-component gives the desired expression in terms of c and d.
ashhlyn

## Homework Statement

a particle's position is the vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j where c and d are positive constants. find the expression for the x-component of the velocity (for time t>0) when the particle is moving in the x-direction. you should express your answer in terms of variables c and d.

## Homework Equations

(vector)r=(ct^2-2dt^3)i+(4ct^2-dt^3)j
is the only given equation

## The Attempt at a Solution

I'm confused on what this problem is asking
I can derive the position vector to get v=(2ct-6dt^2)i+(8ct-3d^2)j but what is the question asking? I thought the x-component would be 2ct-6dt^2 but that was wrong. thank you much for any help

EDIT: when I put the wrong answer in the hint is "first fine the velocity vector and use this to determine the times when the particle is traveling in the x direction)

ashhlyn said:
when the particle is moving in the x-direction
I.e., at a time when there is no other component to the velocity.

haruspex said:
I.e., at a time when there is no other component to the velocity.
ahh thank you! Set Vy equal to zero, solve for t, and put back into Vx. I got the right answers thanks much

## 1. What is the formula for finding the x-component of velocity?

The formula for finding the x-component of velocity is vx = v * cos(θ), where v is the magnitude of the velocity vector and θ is the angle between the velocity vector and the x-axis.

## 2. How do you find the x-component of velocity from a velocity vector?

To find the x-component of velocity from a velocity vector, you can use the formula vx = v * cos(θ), where v is the magnitude of the velocity vector and θ is the angle between the velocity vector and the x-axis.

## 3. Can you explain the concept of x-component of velocity?

The x-component of velocity is the component of a velocity vector that is parallel to the x-axis. It represents the speed and direction of an object's motion in the horizontal direction.

## 4. How is the x-component of velocity different from the y-component of velocity?

The x-component of velocity and the y-component of velocity are different in terms of the direction they represent. The x-component represents the horizontal motion of an object, while the y-component represents the vertical motion. They can also have different magnitudes and can be calculated using different formulas.

## 5. In what situations would you need to find the x-component of velocity?

The x-component of velocity is useful in situations where an object's motion is only in the horizontal direction, such as projectile motion or motion along a horizontal surface. It can also be used to calculate the net force acting on an object in a specific direction.

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