# Trouble with a basic one-dimensional motion problem

1. Mar 10, 2013

### brizznook

1. The problem statement, all variables and given/known data
A red car and a green car, identical except for the
color, move toward each other in adjacent lanes and parallel to an x
axis. At time t 0, the red car is at xr 0 and the green car is at xg
220 m. If the red car has a constant velocity of 20 km/h, the cars pass
each other at x 44.5 m, and if it has a constant velocity of 40 km/h,
they pass each other at x 76.6 m.What are (a) the initial velocity
and (b) the constant acceleration of the green car?

2. Relevant equations
v=vo+at
x-xo=vot+(1/2)at2

3. The attempt at a solution
The only things I am able to obtain by myself are that the green car will be 175.5 m after 8 seconds and it will be at 143.4 m after 6.9 seconds. After that, all of the equations I know or can derive from the two shown will contain at least two variables. I have no idea where to go from there. I know the solutions (according to my solutions manual):

a. vo= -13.9 m/s
b. a = -2.0 m/s2

but I haven't the slightest of clue as to how to reach them. Math is not my strongest suit.
Any help is appreciated. Thanks!

Last edited: Mar 10, 2013
2. Mar 10, 2013

### rude man

Case 1: red car v = 20: what is x(t) for the green car? for the red car?
When they meet at t = t1, x(green) = x(red) = 44.5

Case 2: red car v = 40: what is x(t) for the green car? Same as before?
for the red car? When they meet at t = t2, x = 76.6

4 equations, 4 unknowns: t1, t2, v_0 and a.

Hint: t1 = 44.5/20 and t2 = 76.6/40. Avoids quadratics!