Question

the motion of an object is given parametrically by the equations x=t^2_3t & y=t^3_2t. find all times and locations in which the particle has only vertical and horizantal motion.

Answer 1

x will have horizontal and the y will have vertical
so i believe when x'=0 this will be the horizontal
x'=2t-3=0|
2t=3
t=3/2
WHEN t=3/2 X=9/4-9/2=9/4-18/4=-9/2
when y=t^3-2t
y'=3t^2-2=0
3t^2=2
t^2=2/3
t=sqrt(2/3)
Y(sqrt(2/3))=2/3(sqrt(2/3))-2(sqrt(2/3))
sqrt(2/3)(-4/3)=Y

Answer 2

X=3/2 Y=-4/2(sqrt(2/3))

Answer 3

-4/3(sqrt(2/3))=Y