Quick Review 3-2

Unit 3 - Objective 2 - Parametric Equations - Velocity and Acceleration

Example 1
Curvilinear motion is an object moving in a plane along a specific path. To find the velocity of an object whose coordinates are given in parametric form, find its x-component of velocity by determining dx/dt and its y-component of velocity by determining dy/dt.

Once these are evaluated at a specific time, you can then find the resultant velocity from

The direction, , in which the object is moving is found from

Similarly for acceleration: x-component of acceleration

 Remember: If s(t) = f(t) is a position or distance functions, then v(t) = s'(t) = is the velocity function, and a(t) = s''(t) = is the acceleration function.

Sometimes the x and y coordinates of a point on a curve are given as functions of t. This is parametric form and t is the parameter.

Try it!

Given

Find the magnitude and direction of the velocity when t = 1.

magnitude of the velocity:

direction of motion:
 is in the 1st quadrant because and are both positive.

Example 2

Find the magnitude and direction of (a) velocity vector and (b) acceleration vector at time t = 1.

magnitude of the velocity:

direction of motion:
 is in the 4th quadrant because is positive and is negative.

magnitude of acceleration:

direction of acceleration:

 is in the 1th quadrant because and are both positive.