Question

Hi,
Could you please help me with the following problem I'm trying to solve without success:
John and Jim are racing around a circular track in sports cars. The track has a radius of 400 M. John is leading the race by half a lap and both cars are initially traveling at 60 M/s. Jim than begins to accelerate (acceleration not given). After 50 seconds Jim catches up with John. What was Jim's acceleration ?

Thank You

Answer 1

Since Jim is 200m behind John (0.5*400m) then covering that distance in 50s is going to be 200m/50s.

Answer 2

Thanks for your reply. Actually I should have said angular acceleration, not acceleration.

Answer 3

Sorry was in another window.

Answer 4

Hmmm. This seems like a physics question.

Answer 5

So have you seen an equation that goes something like: \[a=v ^{2}\div r\]

Answer 6

or \[a=w ^{2}r\]

Answer 7

Yes I have

Answer 8

Ok so you are dealing with tangential and angular acceleration with those equations right?
Those are the two things that are going to make up your angular acceleration.

Answer 9

that is correct

Answer 10

excuse me velocity not accelleration, but I think you knew what I meant.

Answer 11

So you have another equation that goes something like this:
\[a= 4\pi ^{2}r \div T ^{2}\]

Answer 12

Since we know that Jim has to increase his velocity by 4m/s to catch up to John in 50 seconds. This would make his tangential velocity 64m/s.

Answer 13

We also know the radius of the track 400m.

Answer 14

So \[a=\left( 64m/s \right)^{2}\div 400m\]

Answer 15

So the angular acceleration should be \[9.30909091m/s ^{2}\]

Answer 16

I think . . . It's been a loooong time since physics so take that answer with a grain of salt. Check into the physics forum to be sure I'm getting my equations right.

Answer 17

Thank You anyway. I'll try with the Physics forum