Ashley -
Without knowing the rate at which your friend's car accelerates or
deccelerates, there's no way to figure out exactly how far the car
would need to go to get up to 83 mph or back to 0. But we can answer
this question... Can the car get up to 83 and back to 0 within 1 mile?
First, we'll assume the car spends exactly 1/2 mile accelerating
and 1/2 mile deccelerating. So the second 1/2 mile is exactly the same
as the first 1/2 mile, just with the car slowing down instead of
speeding up. We'll also assume that the car accelerates and
deccelerates at a constant rate. In this case we can use a couple of
equations about how things move:
total distance = 1/2 x acceleration x time x time
final velocity = acceleration x time
Plugging in your numbers for just the first 1/2 mile (accelerating up to 83), we have:
1/2 = 1/2 x acceleration x time x time
83 = acceleration x time
We can plug the second equation into the first one to get:
time = 1/83 hrs (43 seconds)
So your friend would have to be able to go from 0 to 83 in 43
seconds. For the second 1/2 mile, it's the opposite - he has to go from
83 to 0 in 43 seconds. Sine this is a fairly reasonable idea, I think
you should start looking for another defense.
-Tamara & Tim
(published on 10/22/2007)
