Car and truck velocity question

  • Thread starter vicsic
  • Start date
  • #1
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Question:
A car is initially 4.0km/h south of a gas station and is moving at a constant speed of 55km/h due north. A truck is initially 6.0km north of the gas station and is moving at a constant speed of 45km/h due south. How far are the vehicles from the gas station when they pass each other?

Formulas:
V=d/t

Attempt at solution:
So I said:

Car
D=4.0km south
V=55km/h north

Truck
D=6.0km north
V= 45km/h south

Now I had the idea of making the times equal,

So I calculated the time for the car:
Tcar= d/v = 4.0/55= 0.073h
Ttruck = d/v = 6.0/45=0.13h

From here I am stuck I tryed subtracting the times, but could get any further. Help from this point would be awesome.

I have done a little diagram attached
ImageUploadedByPhysics Forums1361134571.226902.jpg
 

Answers and Replies

  • #2
34,843
11,012
You calculated the time difference as seen at the gas station. This is not relevant for the task here.
Can you express their position as function of time?
 
  • #3
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Would that be t=d/v=d/v??
 
  • #4
34,843
11,012
That would be the time to travel some specific distance.
No, what I mean is an equation of the type x(t)=....
You plug in the time t, and get the position x (relative to the gas station) at that time t.
 
  • #5
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like x(t)=changeinD/change in v
 
  • #6
34,843
11,012
There is no change in v.

A simple example: Imagine I start 10km in front of from the gas station (seen by an arbitrary direction) and move with 20km/h. In that case, my position is given by x(t)=-10km + 20km/h*t
For t=0, this givex x(0)=-10km, as expected.
1/2 hour later, I am at x(1/2 h)=-10km + 20km/h * 1/2 h = -10km + 10km = 0 - in other words, directly at the gas station.

Can you find similar equations for your vehicles?
Afterwards: What means "passing" for their positions?
 

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