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

[mslena79]

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!

 

[learningphysics]

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

 

[mslena79]

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

 

[learningphysics]

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.

 

[mslena79]

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

 

[learningphysics]

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.

 

[mslena79]

thanks, the textbooks never have examples like the ones you have to do in the homework, it makes it very difficult.

 

[learningphysics]

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.