1. Position Vector Equation for an Object moving with a constant velocity
Discrete Math Section 12.3 Use vector and parametric equations to describe motion in a plane
Position Vector Equation for an Object moving with a constant velocity
(x,y) = (xo,yo) + t <a,b>
(xo,yo) is the original position at time 0
<a,b> is the velocity vector
t is the time
(x,y) is the final position at time t

2. examples
An object started at (6,-1) and has a velocity of <2,3>. Find its vector equation and position after 4 seconds.
Find the vector equation of an object that travels from the point A(4,1) to B(-2,5) in one second.

3. (x,y) = (xo,yo) + t <a,b>
A vector equation can be broken down into two parametric equations. Parametric Equations x = xo + at y = yo + bt example: Find the parametric equations for (x,y) = (4,-2) + t<-5,9>

4. example
An object moves with a constant velocity so that its position at time t is given by
(x,y) = (1,1) + t<-1,1>. When and where does the object cross the circle (x – 1)2 + y2 = 5 ?

5. example
Megan and Matt follow the paths indicated by the vector equations (x,y) = (-10,10) + t<4,1> and (x,y) = (20,0) + t<-2,3>.
A. Where do the paths cross?
B. Will they collide?

6. Assignment
Page 435
Problems 1,2,4,10,12,14,17,20,22,23
38ec