Two cars in different directions

[Dave25]

Homework Statement

Two cars drive on a straight highway, at time t= 0, car 1 passes mile marker 0 traveling due east with a speed of 20 m/s. At the same time, car 2 is 1 km east of mile marker 0 traveling at 30 m/s due west. Car 1 is speeding up with an acceleration of magnitude 2.5 m/s^2, and car 2 is slowing down with an acceleration of magnitude 3.2 m/s^2. (a) Write x versus t equations of motion for both cars, taking east as the positive direction. (b) Also, at what time do the cars pass next to one another?

Homework Equations

xf= xi + vi * t + 1/2 at^2

The Attempt at a Solution

x1= (20 m/s) + (1.25 m/s^2) t^2

x2= (1000m) + (-30 m/s) + ( 1.6 m/s^2) t^2

I know this is the right equation for part a.

I just need to know the final answer for part b. Thanks.

 

[LowlyPion]

Don't you just set x1 = x2 and solve?

 

[Dave25]

Yep. Thanks. I don't know what I was thinking, but I should have seen that. I got 24 seconds. I am pretty sure that is right. Well, it's either 24 s or 118 s and 24 sounds better.

 

[ideasrule]

No, both solutions are physically meaningful. Think about it: after car 2 comes to a stop, it starts gaining speed in the other direction, which means...

24 m/s is the right answer, but you can't reject 118 s simply because it doesn't sound good. There's a reason that it's a solution.

 

[bucher]

The 24 second mark isn't necessarily the "better" time, it's just the first time that the cars pass. Since Car B is accelerating faster than Car A, it will eventually (in 118 seconds) pass Car A again. Both of the times are correct.