What is the relative velocity of two cars traveling in the same direction?

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Homework Help Overview

The problem involves two cars, A and B, traveling in the same direction, with car A positioned 186 meters behind car B. The speeds of the cars are given, and the question is about the time it takes for car A to catch up to car B.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of relative velocity and the equations of motion to determine the time for car A to catch car B. There are differing interpretations of how to apply the concept of relative velocity, with some suggesting the sum of velocities and others the difference.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some have provided calculations based on their interpretations, while others question the validity of those approaches. There is no explicit consensus on the correct method or answer yet.

Contextual Notes

Participants note that the problem's context may differ if the cars were traveling in opposite directions, which introduces additional considerations for relative velocity. There is also mention of the challenge posed by textbook examples not aligning with homework problems.

mslena79
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Homework Statement


Two cars, A and B, are traveling in the same direction, although car A is 186m behind car B. The speed of A is 24.4m/s, and the speed of B is 18.6m/s. how much time does it take for A to catch B?



Homework Equations


Va+Vb=Vab, x=1/2(V0x+Vx)t


The Attempt at a Solution



Va=24.4 m/s, Vb=18.6m/s, Vab=43.0m/s,
186m=1/2(24.4m/s+43.0m/s)t
t=5.52s, Just not sure if this is right!
 
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No it isn't right... I don't understand the equations:

Va+Vb=Vab, x=1/2(V0x+Vx)t

how are you getting them?

you can just get the equation for the position for car B as a function of time... get the equation for car A... and set them equal.

You can also do it with relative velocity... in which case

186 = (velocity of A with respect to B)*t
 
for relative velocity, velocity of A with respect to B is Va+Vb=Vab (24.4m/s+18.6m/s=43.0m/s).
186m=(43.0 m/s)*t
t=4.33s
 
mslena79 said:
for relative velocity, velocity of A with respect to B is Va+Vb=Vab (24.4m/s+18.6m/s=43.0m/s).
186m=(43.0 m/s)*t
t=4.33s

Relative velocity is the difference, not the sum of the two velocities.
 
Oh, it is not clear from my text. So, (24.4m/s-18.6m/s=5.8m/s)
186m=(5.8m/s)t
t=32.1s
 
mslena79 said:
Oh, it is not clear from my text. So, (24.4m/s-18.6m/s=5.8m/s)
186m=(5.8m/s)t
t=32.1s

yup. that's right.
 
thanks, the textbooks never have examples like the ones you have to do in the homework, it makes it very difficult.
 
mslena79 said:
thanks, the textbooks never have examples like the ones you have to do in the homework, it makes it very difficult.

One thing I wanted to mention, if the two cars were going in opposite directions, this this is what would happen... if we take east as positive, west as negative... let's say A is going east. And B is going west. So A's velocity is 24.4m/s B's velocity is -18.6m/s. So A's velocity with respect to B is (24.4 - (-18.6)) = 43m/s... so if they were going in opposite directions, the numbers add... And then you'd get 4.33s like you did before...

But yeah, for your question the answer is 32.1s, since they're going in the same direction.
 

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