What were Maggie and Judy's respective accelerations and maximum velocities in the following problem:
Setting a world record in a 100 m race, Maggie and Judy cross the finish line in a dead heat, both taking 12.0 s. Accelerating uniformly, Maggie took 2.00 s and Judy 2.60 s to attain maximum speed, which they maintained for the rest of the race.
If acceleration is given by a, u is the initial velocity, v is the final velocity, t is the time taken and s is the distance traveled, we have:
v = u + at
s = ut + (1/2)at^2
Here, Maggie and Judy cross the finish line of a 100 m race in 12 s.
Maggie attained the maximum speed in 2 seconds which was maintained for the rest of the time.
Let the acceleration be Am, Vmax = Am*2, S = (1/2)*Am*4 = 2*Am
For the rest of the distance 100 - S = 2*Am*10
100 - 2*Am = 20Am
=> 100 = 22Am
=> Am = 100/22 m/s^2
Vmax = 100/11 m/s
Maggie's acceleration was 100/22 m/s^2 and her maximum velocity was 100/11 m/s
For Judy, Vmax = 2.6*Aj, S = (1/2)*Aj*(2.6)^2 = 3.38*Aj
100 - 3.38Aj = 2.6*Aj*9.4
=> 100 = 27.82*Aj
Aj = 100/27.82 m/s^2
Vmax = 260/27.82 m/s
Judy's acceleration was 100/27.82 m/s^2 and her maximum velocity was 260/27.82 m/s