# Two cars

1. Sep 11, 2009

### seraphimhouse

1. The problem statement, all variables and given/known data

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.6 m/s2. At the same instant a truck is 11.1 m down the road and traveling with a constant speed of 9.4 m/s.

(a) How far beyond the traffic signal will the automobile overtake the truck?
(b) How fast will the automobile be traveling at that instant?

2. Relevant equations

X-Xo = Vo + 1/2at^2
X-Xo = 1/2(Vo + V)t

3. The attempt at a solution

Using X-Xo = Vo + 1/2at^2 I got
X = (1.3 m/s^2)t^2 for the car

Using X-Xo = 1/2(Vo + V)t I got
x = (4.7m/s)t + 11.1m for the truck

I set them equal to each other and found the algebra to be difficult (I stink at algebra) so instead I made the truck's equation x = (4.7m/s)t and eliminated the 11.1m and once again set the truck and the car's equation equal to each other. I got the time to be 3.62s and the distance from the light to be about 28.0m, but was obviously wrong. Can it be my equations for constant acceleration that may be wrong?

2. Sep 11, 2009

### Jebus_Chris

Algebra is kinda important.
Just use the quadratic formula once you set them equal to each other.

3. Sep 7, 2010

### pongo38

your first relevant equation should have a t after the vo, although it makes no difference in this case. Your truck's equation x = (4.7m/s)t should be 9.4 m/s x t. How do you get 4.7t ?
Could you show your working, because I don't see how you can eliminate a quadratic relationship if it exists.