Acceleration again

1. Sep 10, 2004

Omid

Two cars are in a drag race. The first starts and continues to uniformly accelerate up to the finish line some time later. The second car follows the first out of the starting box 1s afterwards traveling exactly as it did. Will the cars be the same distance apart throughout the race? How much time will there be between their successive crossing of the finish line ?

I think the answer to the first question is yes, and to the second one : 1s.
What do you think about that ?
Thanks

2. Sep 10, 2004

faust9

If this where changed a little to say "Two balls are dropped from the same height but with a 1 second delay between the release of each ball" Would the distance between the balls remain constant?

3. Sep 10, 2004

Omid

Yes it would remain constatn.

4. Sep 10, 2004

faust9

No... What is the definition of acceleration?

5. Sep 10, 2004

Tide

Are you sure?

6. Sep 10, 2004

faust9

7. Sep 10, 2004

BobG

The answer to the first is 'No'. The answer to the second is '1 sec'.

If the cars are accelerating at a constant rate, they cover more ground each second than they did the previous second.

If they are accelerating at 2 m/s^2:

After 1 sec, the first has moved 1 meter - the second 0.
After 2 sec, the first has moved 4 meters - the second 1 meter.
After 3 sec, the first has moved 9 meters - the second 4 meters.
And so on.

8. Sep 10, 2004

faust9

$$\vec{a}=\frac{dv}{dt}$$

At any given time the velocities of the two falling bodies will not be the same. The one dropped first will have a greater V at time 1 than the second body. If you look at acc. of each body with respect to the earth the acc. will be the same. Look at the acc. of one body with respet to the other and you see that the acc is constantly changing.

$$\vec{a}_{rel}=\frac{dv_{rel}}{dt}$$

When doing comparisons like this you need to look at the bodies in relation to each other and not in relation to a third body (usually).

Good luck.

9. Sep 10, 2004

Omid

Thanks a lot

10. Sep 10, 2004

Omid

So they are closest to each other after first second, aren't they ?

11. Sep 10, 2004

Tide

Sorry - I was asking Omid who stated the separation would be constant. I didn't notice you had slipped in there before I posted it.