Solve motion problems using parametric and vector-valued functions

A particle moves in a curve along the xy plane that can be described by the equation and is moving in the x-coordinate at a rate of . If the point is at , what is the rate of change in the y-coordinate with respect to time?

Find the acceleration vector at

A particle moves so that at any given time, t, the position of the particle can be described by its parametric equation by  and 

What would be the magnitude of the velocity vector at ?

A particle moves so that at any given time, t, the position of the particle can be described by its parametric equation by and 

Find the magnitude of the velocity vector at  

A particle moves so that at any given time, t, the position of the particle can be described by its parametric equation by  and 

. What would be the distance travelled by the particle from  to ?

A particle moves in a curve along the xy plane that can be described by the equation  and is moving in the y-coordinate at a rate of . If the point is at (13,27), given that the rate of change in the x-coordinate with respect to time is , what would be the magnitude of the particle's velocity?

A particle moves in a curve along the xy plane that can be described by the equation  

and is moving in the y-coordinate at a rate of . If the point is at , what is the rate of change in the x-coordinate with respect to time?

Find the maximum acceleration attained on the interval when the particle's velocity can be described by the equation 

A particle moves long the x-axis so that at time t ≥ 0, its position can be described by the equation . At what time, t, is the particle at rest?

The position of a particle is given by and given that the magnitude of the velocity vector at   is  

find the total distance travelled by the particle from   to  

A particle moves in the xy plane so that at any time t, the position of the particle can be described by the parametric equations

Find the acceleration vector at

The position of a particle is given by and

Find the magnitude of the velocity vector at  

 A particle moves along the curve and is moving in the y-coordinate at a rate of 2 units/second. What would be its rate of change in the x-coordinate when the point has an x-coordinate of 4.