The position of particle P at time t is given by {x=t, y=3t-1}

Question

and the position of particle Q at time t is given by {x=4t-(t^2), y=t+1}

a) Sketch both paths as well as possible. Be sure to label the paths with the particles (P and Q) traveling on each of them.

b) Find the two point of intersection of the paths exactly using algebra.

c) Do the particles ever collide? Support your answer (one of {Yes|No}) with a reason

Answer 1

the paths should not be too hard to sketch. Eliminating t, we have

y = 3x-1
x = 4(y-1) - (y-1)^2

http://www.wolframalpha.com/input/?i=plot+y+%3D+3x-1%2C+x+%3D+4%28y-1%29+-+%28y-1%29^2+

now (b) and (c) become easy, though you should probably work on them using the parametric equations; you can verify your answers with the x-y equations.