Calculating Separation of Car and Truck

[egadda2]

Homework Statement

A car and a truck are heading directly toward one another on a straight and narrow street, but they avoid a head-on collision by simultaneously applying their brakes at t=0 . The resulting velocity-versus-time graphs are shown in the figure .

What is the separation between the car and the truck when they have come to rest, given that at t = 0 the car is at x = 24 and the truck is at x = -44 ? (Note that this information determines which line in the graph corresponds to which vehicle.)

Homework Equations

x_f = x_i + 1/2 (v_f + v_i)$$\Delta$$t

The Attempt at a Solution

x_car = 25 m + 1/2 (0 + 10 m/s)(2.5s) = 36.5
x_truck = -44 + 1/2 (0 - 15 m/s)(3.5s) = -70.25

x_truck - x_car = -33.75 m?

 

[Jebus_Chris]

The area under a curve is the displacement. Now look at the graph and figure out which one is the car and truck. The car is at a positive position and heading towards the truck which has a negative position which would give it a ________ velocity.

 

[semc]

I believe displacement and velocity are vectors properties therefore positive and negative describe the direction of the object.
Firstly, the 1st equation should be (initial distance - distance traveled during the deceleration) because the object is getting closer and closer to the origin where you measure the distance of 25m. The same for the second equation, it should be -44-(-26.5).Lastly, the question is asking for the separation of both the object so there should not be a negative sign.