A Basic Kinematics Problem - Please find my error

[Lank]

Homework Statement

Speedy Sue, driving at 30.0m/s, enters a one-lane tunnel. She then observes a slow-moving van 155m ahead traveling at 5.00m/s. Sue applies her brakes but can only accelerate at -2.00m/s^2 because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of the closet approach between Sue's car and the van.

Homework Equations

Average A = Velocity final - Velocity initial (change in V) / Time final - Time initial (change in T)
D= .5(Vi + Vf) x t
Average V = (change in X) / (change in time)

The Attempt at a Solution

Alright guys, the answer in the back of the book and other Googled results say that I did this the wrong way, but I can't see my error. Here we go:
Speedy Sue is decelerating as quickly as possible, thus her intended final velocity is 0. We know her initial velocity which is 30m/s, and we know her acceleration which is -2m/s^2.
So the formula for Sue is (A) = (Vf - Vi) / (T elapsed)
(-2) = (0-30) / (T elapsed)
(-2)(T elapsed) = (-30)
(T elapsed) = 15seconds. Then I plugged this into the distance formula: D= .5(Vf + Vi) x t or D = .5(30+0) x 15 = 225 meters
So, Sue needs 225 meters and 15seconds to come to a stop (and avoid the wreck).

Now I gave the van 15seconds before it would get hit, while he has a constant velocity of 5m/s. So after Sue saw the van, the van went 75 meters in 15seconds. Add 75 meters to the initial 155 meters in between the two drivers, and we get 230 meters. 5 meters short of a wreck. I don't see my error, and if I messed up then it must have been at the beginning with my formula selection. Please enlighten me, thanks all.

 

[alphysicist]

Hi Lank,

Homework Statement

Speedy Sue, driving at 30.0m/s, enters a one-lane tunnel. She then observes a slow-moving van 155m ahead traveling at 5.00m/s. Sue applies her brakes but can only accelerate at -2.00m/s^2 because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of the closet approach between Sue's car and the van.

Homework Equations

Average A = Velocity final - Velocity initial (change in V) / Time final - Time initial (change in T)
D= .5(Vi + Vf) x t
Average V = (change in X) / (change in time)

The Attempt at a Solution

Alright guys, the answer in the back of the book and other Googled results say that I did this the wrong way, but I can't see my error. Here we go:
Speedy Sue is decelerating as quickly as possible, thus her intended final velocity is 0. We know her initial velocity which is 30m/s, and we know her acceleration which is -2m/s^2.
So the formula for Sue is (A) = (Vf - Vi) / (T elapsed)
(-2) = (0-30) / (T elapsed)
(-2)(T elapsed) = (-30)
(T elapsed) = 15seconds. Then I plugged this into the distance formula: D= .5(Vf + Vi) x t or D = .5(30+0) x 15 = 225 meters
So, Sue needs 225 meters and 15seconds to come to a stop (and avoid the wreck).

Now I gave the van 15seconds before it would get hit, while he has a constant velocity of 5m/s. So after Sue saw the van, the van went 75 meters in 15seconds. Add 75 meters to the initial 155 meters in between the two drivers, and we get 230 meters. 5 meters short of a wreck. I don't see my error, and if I messed up then it must have been at the beginning with my formula selection. Please enlighten me, thanks all.

The collision occurs before the car has a chance to slow down to a stop, so finding the position when v=0 does not answer the question.

Instead consider this. A collision occurs when two objects are at the same place at the same time. Does that help to set up the problem?

 

[Lank]

Thanks, I made a wrong assumption at the start, Final V = 0 was too good to be true. I just set both motion equations for each object equal to each other and solved.