# Average acceleration race horse problem

1. Dec 12, 2007

### galuda

1. The problem statement, all variables and given/known data
Secretariat ran the Kentucky derby with time for the quarter mile of 25.2s, 24s, 23.8s, and 23s. Assuming that secretariat's instantaneous speed at the finish line was the same as the average speed during the final quarter mile, find his average acceleration for the entire race.

2. Relevant equations

average velocity=distance/time
acceleration=change in velocity/time

3. The attempt at a solution Got the first part of this problem right which was just what was his average speed during the first quarter mile in ft/s. That was just 1320ft/25.2. Now the way i read this part of the question was using his average velocity for the final quarter mile which would be 1320/23 = 57.3913ft/s find his average acceleration for the entire race which would then be 57.3913/average time for all 4 1/4mile runs. However the answer i get of 2.391m/s^2 is not the right answer. Can anyone tell me how I am reading this question wrong?

2. Dec 12, 2007

### loonychune

57.3913 $$\div$$ 24 $$\neq$$ 2.391 METRES S$$^{-2}$$.

Rather it is equal to 57.3913 FEET S$$^{-2}$$.

What you want to do then is convert into metres per second squared
(I would usually stick to metres from the very start... 1609 metres per mile)

I'm assuming the method is right, for the horse accelerating from speed 0 to the
final speed.

3. Dec 12, 2007

### loonychune

Sorry i mean it is equal to 2.391 FEET $$^{-2}$$

4. Dec 12, 2007

### loonychune

Sorry i mean it is equal to 2.391 FEET $$^{-2}$$.

I'm just wondering also whether you might want to divide by the sum of the times if you were looking at it in the sense that he starts at speed 0 and gets to a speed 57.3913 (as he does this over the entirity of the race, and i assume that's what's meant by average acceleration)

5. Dec 13, 2007

### galuda

Well they want the answer in ft/s^2 which is why I didn't convert to meters, but I've also tried it using your last posted method prior to asking for help and that doesn't work either. I think the question is just worded poorly, because I've tried it every way I can think of trying to make the words work, but it just doesn't work.

Thanks though.