00:01
So for this problem we've been given the quarter mile segments for secretariat at the kentucky derby and for part a we need to find his average speed during each quarter mile segment.
00:11
So speed is equal to distance over time.
00:16
So for the first segment, we get the speed is equal to quarter of a mile over 25 .2 seconds.
00:20
If we calculate, we calculate it first seg, we get the speed is equal to quarter of a mile over 25 .2 seconds.
00:32
That we get that he has an average speed of 9 .92 times 10 to the minus 3 miles per second and we can just times that by 3 ,600 times by 3 ,600 and that gets us to a more reasonable 35 .7 miles per hour.
01:10
And then the second segment we do exactly the same thing.
01:14
We get s is equal to a quarter mile over 24 .0 seconds and that comes out to be 0 .0104 miles per second which is as we did before, multiply by 3 ,600 and we get 37 .5 miles per hour.
01:51
In the third segment, we get s is equal to a quarter mile over 23 .8 seconds, and that is equal to 0 .105 miles per hour.
02:19
A second and finally sorry and then we times out by 3 ,600 yet these obviously you can have them in whatever form you want just for just to be helpful i've put them in miles per hour because they're more sort of tangible concept and then for the fourth segment we have s is equal to a quarter mile over 23 .0 so our s is therefore equal to 0 .0109 miles per second and that again multiplied by 3 ,600 gives us 39 .1 miles per hour.
03:14
So that's part a done and then for part b it asks us assuming the secretarets instantaneous speed at the finish line was the same as his average speed during the first quarter mile find his average acceleration for the entire race so we know that the acceleration is equal to the velocity final minus the velocity initial over time over time total we'll call it and so his velocity initial it says is zero zero miles per hour and his velocity final says is the same as his average speed in the first quarter mile, which we calculated as...
04:00
Scroll up here.
04:06
We calculated that as 35 .7 miles per hour.
04:17
So therefore our acceleration is equal to 35 .7 minus 0 over the t total, which is 25 .2...