Setting a world record in a 100m race maggie and judy cross...

Setting a world record in a 100m race, Maggie and Judy cross the finish line in a dead heat, both taking 9.0s to accelerate uniformly. Maggie took 2.00s and Judy took 2.40s to attain maximum speed, which they maintained for the rest of the race. a) What was the acceleration of each sprinter? b) What were their respective maximum speeds? c) By how much was Maggie ahead?

Transcript

0:00 Hello.

00:01 So let's start with maggie.

00:08 Both start from rest.

00:09 So the initial speed is zero.

00:10 So for maggie, initial speed is zero.

00:15 Acceleration is a.

00:16 We don't yet know the value.

00:19 And time is two seconds.

00:25 So the velocity at the end of two seconds will be given by u plus 80, which is zero plus two of acceleration.

00:34 So the velocity is 2a meters per second.

00:42 The distance cover within the 2 seconds can be given by the formula t into bracket initial plus final velocity over 2, which is the time 2, initial is 0.

00:54 Final is what we are found as 2a all over 2.

01:00 So our distance traveled is also to a.

01:05 So at the end of the two seconds, the velocity, final velocity is 2a and distance traveled is also 2a meters.

01:26 Now, it took 9 seconds and also, we have 7 seconds left to run this portion of the race.

01:40 If it took 9 seconds for the whole race and we spent 2 on the first part, then we have only 7 seconds for the final part.

01:52 Now, the time taking, we know velocity equals distance over time.

02:01 And so time taking can be calculated as distance over velocity.

02:07 So the time taking to travel the second part, which is seven seconds, is equal to the distance to be traveled, which is going to be 100 minus 2a.

02:19 Remember, we are traveling this distance here now.

02:22 So that is going to be the entire distance which is hundred minus this distance here which is 2a so what is left here is hundred minus 2a so we travel the distance of hundred minus 2a in seven seconds what will be the velocity now the velocity the constant velocity that will be used to travel this last distance is the final velocity that was attained which is 2a so we are left to with this equation to solve so we have 100 minus 2a equals 14a, 100 equals 16a, acceleration is 6 .25.

03:28 So acceleration equals 16, sorry, 6 .25 meters per second.

03:38 We do the same for judy.

03:42 For judy, again, she starts from rest.

03:45 Her acceleration is 2 .4 meters per second.

03:52 Sorry, her acceleration is a.

03:54 We don't know acceleration.

03:55 It's a time that is 2 .4 meters per second.

03:58 Acceleration is unknown.

04:00 Time is 2 .4.

04:02 So we can find a final speed at the end of the two seconds, which will be initial speed plus acceleration times time...