In a 100 m race, Maggie and Judy cross the finish line in a dead heat, both taking 10.6 s. Accelerating uniformly, Maggie took 2.20 s and Judy 2.90 s to attain maximum speed, which they maintained for the rest of the race.

A) What was Maggie's acceleration?
B) What was Judys acceleration?
C) What is Maggies maximum speed?
D) What was Judys maximum speed?
E) What distance had Maggie run at the 6.40 s mark?
F) What distance had Judy run at the 6.4 s mark?

A) To find Maggie's acceleration, we can use the equation of uniform acceleration:

acceleration = (final velocity - initial velocity) / time taken

From the given information, we know that Maggie took 2.20 s to attain her maximum speed, and her final velocity is the maximum speed. However, we do not have the initial velocity.

We can solve for the initial velocity using the formula:

initial velocity = final velocity - (acceleration * time taken)

Since Maggie crossed the finish line in a dead heat with Judy, we know that they both took the same time of 10.6 s. Therefore, the time taken to reach maximum speed for Maggie (2.20 s) can also be used as the time taken for the entire race (10.6 s) since both are equal.

Now, we can solve the equation:

initial velocity = final velocity - (acceleration * time taken)

initial velocity = final velocity - (acceleration * 2.20)

10.6 = 0 - (acceleration * 2.20) (We assume the initial velocity is 0, since the problem does not state otherwise.)

-2.20 * acceleration = 10.6

acceleration = 10.6 / -2.20

acceleration ≈ -4.8182 m/s^2

Therefore, Maggie's acceleration is approximately -4.8182 m/s^2.

B) Similarly, we can find Judy's acceleration using the same method.

initial velocity = final velocity - (acceleration * time taken)

initial velocity = final velocity - (acceleration * 2.90)

10.6 = 0 - (acceleration * 2.90)

-2.90 * acceleration = 10.6

acceleration = 10.6 / -2.90

acceleration ≈ -3.655 m/s^2

Therefore, Judy's acceleration is approximately -3.655 m/s^2.

C) To find Maggie's maximum speed, we need to use the equation of motion:

final velocity = initial velocity + (acceleration * time taken)

Using the information given, we know:

initial velocity = 0 (assuming)
acceleration = -4.8182 m/s^2
time taken = 2.20 s

final velocity = 0 + (-4.8182 * 2.20)

final velocity = -10.600 (negative sign indicates the direction)

Therefore, Maggie's maximum speed is approximately 10.600 m/s.

D) Similarly, for Judy's maximum speed:

initial velocity = 0 (assuming)
acceleration = -3.655 m/s^2
time taken = 2.90 s

final velocity = 0 + (-3.655 * 2.90)

final velocity = -10.611 (negative sign indicates the direction)

Therefore, Judy's maximum speed is approximately 10.611 m/s.

E) To find the distance Maggie ran at the 6.40 s mark, we need to find the distance covered during the acceleration phase and the distance covered during the constant speed phase.

Distance during acceleration phase can be calculated using the equation:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Since Maggie's initial velocity is not given, we assume it to be 0.

distance during acceleration phase = (0 * 2.20) + (0.5 * (-4.8182) * (2.20^2))

distance during acceleration phase ≈ -11.5246 m

Distance during constant speed phase can be calculated using the equation:

distance = (final velocity * time)

final velocity = -10.600 m/s (from part C)
time = 6.40 s

distance during constant speed phase = (-10.600 * 6.40)

distance during constant speed phase ≈ -67.84 m

Total distance covered by Maggie at the 6.40 s mark = distance covered during acceleration phase + distance covered during constant speed phase

Total distance covered ≈ (-11.5246) + (-67.84)

Total distance covered ≈ -79.3646

Therefore, Maggie has run approximately 79.3646 m at the 6.40 s mark.

F) Similarly, for Judy's distance at the 6.4 s mark:

distance during acceleration phase = (0 * 2.90) + (0.5 * (-3.655) * (2.90^2))

distance during acceleration phase ≈ -9.7926 m

distance during constant speed phase = (-10.611 * 6.40)

distance during constant speed phase ≈ -67.9424 m

Total distance covered by Judy at the 6.40 s mark = distance covered during acceleration phase + distance covered during constant speed phase

Total distance covered ≈ (-9.7926) + (-67.9424)

Total distance covered ≈ -77.735

Therefore, Judy has run approximately 77.735 m at the 6.40 s mark.