Kinematics passing cars problem

[Amphetamxne]

Homework Statement

A car in the northbound lane is sitting at a red light. At the moment the light turns green, the car accelerates from rest at 2m/s². At this moment there is also a car in the southbound lane that is 200m away and traveling at a constant 25m/s. The northbound car maintains its acceleration until the two cars pass each other.
a. How long after the light turns green do the cars pass each other?
b. How far from the red light are they when they pass each other?

Homework Equations

x = vt + ½at²

The Attempt at a Solution

I know the distance traveled by both cars totals 200m, so I assume this to be x and set vt + ½at² equal to 200. I only know (?) that Car A maintains a constant acceleration of 2m/s² and I only know that Car B travels a constant 25m/s and is 200m away. Does this mean Car B has no acceleration since velocity is constant? If so, I'm confused as to what I'm actually supposed to substitute into the equation. Initially, I tried using:
x = ½ (v_o + v)t
and solved by:
200 = ½(25 + 25)t
t = 8s
but this is not the correct answer.
Any help is appreciated!

 

[hmmm27]

.

 

[gneill]

Hi Amphetamxne, Welcome to Physics Forums!

There are two different cars to track the position of, so that implies you should write a separate equation for each. One has a constant speed (25 m/s) and starts off at some initial position (200 m). Note that this car is heading towards the "origin". Can you write an expression for the position with respect to time for this constant speed car?

The other car starts at position zero (our "origin") with no initial speed but a constant acceleration. Can you write an expression for its position with respect to time?

 

[Amphetamxne]

Hi Amphetamxne, Welcome to Physics Forums!

There are two different cars to track the position of, so that implies you should write a separate equation for each. One has a constant speed (25 m/s) and starts off at some initial position (200 m). Note that this car is heading towards the "origin". Can you write an expression for the position with respect to time for this constant speed car?

The other car starts at position zero (our "origin") with no initial speed but a constant acceleration. Can you write an expression for its position with respect to time?

Hi, thanks.
Would it be something like this?
For Car A with constant acceleration:
X_A = x₀ + v_A0t + ½a_At²
= 0 + 0 + ½ (2.0 m/s²)t²
= ½ (2.0 m/s²)t²

For Car B with constant speed:
X_B = x₀ + v_B0t + ½a_Bt²
= 200 + (25 m/s)t + 0
= 200 + (25 m/s)tSorry if I'm completely wrong, this is my first Physics class and I'm still not completely familiar with all of the formulas or how to use them correctly.

 

[gneill]

Hi, thanks.
Would it be something like this?
For Car A with constant acceleration:
X_A = x₀ + v_A0t + ½a_At²
= 0 + 0 + ½ (2.0 m/s²)t²
= ½ (2.0 m/s²)t²

For Car B with constant speed:
X_B = x₀ + v_B0t + ½a_Bt²
= 200 + (25 m/s)t + 0
= 200 + (25 m/s)tSorry if I'm completely wrong, this is my first Physics class and I'm still not completely familiar with all of the formulas or how to use them correctly.

You've done very well. One thing though, remember that I noted that the constant speed car (car B) was heading towards the origin? What does that tell you about the sign of his velocity? Fix that up and you're good to go --- two equations in two unknowns to solve.

 

[Amphetamxne]

You've done very well. One thing though, remember that I noted that the constant speed car (car B) was heading towards the origin? What does that tell you about the sign of his velocity? Fix that up and you're good to go --- two equations in two unknowns to solve.

Alright, I appreciate the help!