# Position Vector r(t) with Unit Vectors

A point moves in the x,y plane. Position vector r(t), from the origin to the point, gives the location of the point at time, t. Unit vectors are i and j, each 1 unit long in the x and y directions respectively. Write answers assuming units of distance in meters and times in seconds.

Given: r(t)= (2 t^2 + 15) i - (8 t - 9) j

a. On an x,y axis system show r(0) and also r(3), then show vector D drawn

from the head of r(0) to the head of r(3) showing that r(0) + D = r(3).

b. From your drawing, find the magnitude and direction of the vector D.

c. Write the velocity vector, v(t), then write v(3) with polar coordinates.

d. Express the x coordinate as a function of time & make a qualitative graph

of x(t) then repeat for the y coordinate and make a qualitative graph of y(t).