Velocity and Acceleration of a particle

AI Thread Summary
The discussion focuses on determining the position, velocity, and acceleration of a particle described by the given equations for x(t) and y(t). The user has successfully derived the velocity components v(x) and v(y) by differentiating the position functions. To find acceleration, the user needs to differentiate the velocity components. For the time when the horizontal and vertical velocity components are equal, setting v(x) equal to v(y) and solving for "t" is the correct approach. The user also considers solving for when x(t) equals y(t) to explore further relationships between the coordinates.
cougar_21
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Velocity and Acceleration Please Help!

My problem reads:

A particle is observed to move with the coordinates x(t)=(1.5m/s)t + (-0.5 m/s^2)t^2 and y(t) = 6m + (-3m/s)t + (1.5 m/s^2)t^2. What are the particle's position, velocity, and acceleration? At what time(s) are the velocity's horizontal and vertical components equal?

I got the derivative of x(t) and y(t) to get v(x) and v(y). Where do I go from there :confused:
 
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do get the acceleration take the derivative of V(x) and V(y).

For the what time thing, set them equal, solve for "t"?
 
For the second question, solve for x(t) = y(t).
 
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