# With v vs t graph, what is the separation between two vehicles when they come to rest

1. Sep 6, 2009

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

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.)

2. Relevant equations

xf = xi + 1/2 (vf + vi)$$\Delta$$t

3. The attempt at a solution

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

xtruck - xcar = -33.75 m?

2. Sep 6, 2009

### Jebus_Chris

Re: With v vs t graph, what is the separation between two vehicles when they come to

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.

3. Sep 6, 2009

### semc

Re: With v vs t graph, what is the separation between two vehicles when they come to

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 travelled 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 seperation of both the object so there should not be a negative sign.

Last edited: Sep 6, 2009