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.


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