Careful measurements have been made of olympic sprinters in...

Careful measurements have been made of Olympic sprinters in the 100 -meter dash. A simple but reasonably accurate model is that a sprinter accelerates at $3.6 \mathrm{m} / \mathrm{s}^{2}$ for $3 \frac{1}{3} \mathrm{s}$, then runs at constant velocity to the finish line. a. What is the race time for a sprinter who follows this model? b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter's top speed is the same as in part a, what acceleration would he need to run the 100 -meter dash in $9.9 \mathrm{s} ?$ c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by $1 $% ?

Transcript

00:01 Hi, for this question, we have a 100 meter distance, square is s.

00:10 And so we told that the sprinter accelerates for three points at 3 .6 meters per second squared for three points for three one third seconds and then runs on the constant velocity.

00:22 One to find the rest time.

00:25 So first of all, we'll find the distance that the sprinter travels on accelerating in the first instance.

00:35 So, reason s is equal to ut plus half, e t squared.

00:44 S is the distance, used in your velocity.

00:46 Since starts from rest to be zero, t is the time, and a is the acceleration.

00:51 So, s is equal to 0 plus half times the acceleration is 3 .6, times the time, 3, rest by 1 over 3.

01:06 Reda 3, all known by 1 over 3.

01:16 This is the culture and this is equal to 20 meters.

01:23 So that means that the main distance left for the runner to run is 100 minus 20, which is 80 meters.

01:31 So now we need to find the time it takes to run at the constant velocity to the finish line, 18 meters away.

01:40 So now let's find the final velocity of the sprinter during after the acceleration.

01:45 So v is equal to u plus 80.

01:50 V is equal to 0 plus 3 .6 times 3 1 over 3 squared.

02:01 There's no squared there.

02:07 So the velocity will be 12 meters per second.

02:11 So this is the constant velocity runs at.

02:13 So define the time, you have v is equal to distance by by time.

02:16 So time is equal to distance divided by velocity.

02:20 So the time is distance 80 divided by 12, which is equal to.

02:26 And is equal to 20 over 3 seconds so now to find the total time for the race mean to add it to the time of giving us 3 1 over 3 seconds so this 20 divided by 3 plus 3 1 over 3 this be called 10 seconds so that's our time for the first 1 b we have the sprinter once you find out what acceleration the sprinter would need to finish the 100 meter dash in 9 .9 seconds...

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