Velocity and acceleration from a position equation

In summary, The question asks for the velocity and acceleration of a particle moving at a constant velocity in the y-direction while its x-position is defined by the equation x=y^2/6. To find the velocity and acceleration, the equations v=sqrt(vx^2+vy^2) and a=sqrt(ax^2+ay^2) can be used. The method of finding the velocity in the x-direction is to differentiate the x-position equation with respect to x and then plug in the given x-value. For acceleration, since Vy is constant, y"=0 which leaves only the x-direction to consider. The suggested method is to make y a function of t and proceed from there.
  • #1
glid02
54
0
Here's the question:
A particles position is defined by the equation x=y^2/6 and it moves at a constant velocity in the y-direction of 3 in/s. Find the velocity and acceleration when x=6 in.

I know v=sqrt(vx^2+vy^2) and a is found the same way, but I have absolutely no idea how to find the velocity of in the x-direction through the equation.

The only way I can think to do it is find the change in the x position over a very small interval of time and go from there, but I know there's an easier way.

If anyone could give me a starting point it'd be great.

Thanks a lot.
 
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  • #2
well if Vy is constant, y"=0 leaving only the x directions to worry about fpr acceleration.
so can't you just differentiate with respect to x and plug in the x value given? For velocity add the constant as you propose, vector summation.
 
Last edited:
  • #3
yeah, I'm half retarded. I needed to make y a function of t and go from there. Thanks.
 

What is the difference between velocity and acceleration?

Velocity is a measure of an object's speed and direction, while acceleration is a measure of the change in an object's velocity over time.

How do you calculate velocity from a position equation?

Velocity can be calculated by taking the derivative of the position equation with respect to time.

How do you calculate acceleration from a position equation?

Acceleration can be calculated by taking the second derivative of the position equation with respect to time.

Can you have a negative velocity or acceleration?

Yes, both velocity and acceleration can be negative. Negative velocity indicates that an object is moving in the opposite direction of its positive velocity, and negative acceleration indicates that an object is slowing down.

How does the position equation relate to velocity and acceleration?

The position equation shows the relationship between an object's position, velocity, and acceleration. It can be used to calculate any of these variables given the other two.

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