One-Dimentional Kinematics Question

[joeisconfused]

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 20.0 m/s. At the same time, car 2 is 1.0 km east of mile marker 0 traveling at 30.0 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. Write x-versus-t equations of motion for both cars"

Homework Equations

The equation I used was X = Xi + ViT + 1/2 AT^2

Sorry, I'm bad at typing these equations without subscripts or superscripts.

The Attempt at a Solution

I got the equation right for Car 1. However, when I went to solve for Car two, it did not match with the answer key. I plugged in all of the relevant information into the equation:

X = 1000m + (-30 m/s)t + 1/2(3.2 m/s^2)t^2 = 1000m + (-30 m/s)t + (1.6 m/s^2)t^2

Since Car 2 is going towards the 0 marker, the velocity should be zero. However, in order for there to be deceleration, accerleration and velocity should have opposite signs. Since velocity is negative, I made acceleration positive.

However, this doesn't match the textbook answer, which is X = 1000m - (-30 m/s)t - (1.6 m/s)t^2

Am I doing something wrong?

Thanks in advance for taking the time to answer my question!

 

[kuruman]

How about starting with two separate equations (as the problem suggests), one for each car. Fill in the blanks

x₁ =

x₂ =

Then it should be clearer what you're doing.

 

[Fightfish]

Hm...the textbook answer looks wrong; inserting t=1, we would get X = 1028.4m > 1000m, which is clearly not possible given that the car is heading towards the 0 mark.

 

[joeisconfused]

Basically, the first one is simple enough to do without any trouble, and it's the second car that I'm having trouble with. To clear things up:

What I did for Car 1:

x₁ = x_i + v_it + 1/2 at²
x₁ = 0 m + (20 m/s)t + 1/2(2.5 m/s²)t²
x₁= (20 m/s)t + (1.25 m/s²)t²

This answer matched with the textbook answer, so I didn't have any trouble for the first one. I simply plugged in the givens into the equation.

What I did for Car 2:

x₂ = 1000m + (-30 m/s)t + 1/2(3.2 m/s²)t²
x₂= 1000m + (-30 m/s)t + (1.6 m/s²)t²

My reasoning: Since Car 2 is going towards the 0 marker, the velocity should be zero. However, in order for there to be deceleration, accerleration and velocity should have opposite signs. Since velocity is negative, I made acceleration positive.

textbook answer is X2 = 1000m - (-30 m/s)t - (1.6 m/s)t²

Am I doing things incorrectly or is this a textbook error?

Edit: Just saw the above post. Thanks for the response!