in a 100m race, 2 sprinters finish at the same time of 10.2 seconds, accelerating uniformly, sprinter A took 2 seconds to obtain max speed, sprinter B took 3 seconds, they ran their max speed for the remainder of the race, what is the acceleration of each sprinter?

The first runner accelerated for 2 seconds, achieving a velocity of v = at = 2a, which he used for the remainder of the race:

100 = 1/2 a(2^2) + a(2)(8.2)
100 = 2a + 16.4a = 18.4a
a = 5.43m/s^2

similarly for the 2nd runner:

100 = 1/2 a(3^2) + a(3)(7.2)
100 = 4.5 a + 21.6a = 26.1a
a = 3.83m/s^2

To find the acceleration of each sprinter, we can use the following formula:

Acceleration = (Final Velocity - Initial Velocity) / Time

Let's assume the final velocity for both sprinters is V, and the initial velocity is 0 m/s since they start from rest.

For Sprinter A:
Time taken to reach max speed = 2 seconds
Remaining time = Total time - Time taken to reach max speed = 10.2 - 2 = 8.2 seconds

For the first part of the race:
Acceleration of Sprinter A = (V - 0) / 2 = V / 2

For the second part of the race (running at max speed):
Acceleration of Sprinter A = 0 m/s^2 (since the velocity is constant)

For Sprinter B:
Time taken to reach max speed = 3 seconds
Remaining time = Total time - Time taken to reach max speed = 10.2 - 3 = 7.2 seconds

For the first part of the race:
Acceleration of Sprinter B = (V - 0) / 3 = V / 3

For the second part of the race (running at max speed):
Acceleration of Sprinter B = 0 m/s^2 (since the velocity is constant)

So, the acceleration of Sprinter A is V/2 for the first part of the race, and 0 for the second part.
The acceleration of Sprinter B is V/3 for the first part of the race, and 0 for the second part.

To find the acceleration of each sprinter, we can use the formula:

acceleration = (final velocity - initial velocity) / time

Let's calculate the acceleration for each sprinter:

Sprinter A:
Sprinter A took 2 seconds to reach maximum speed. We know that the final time for both sprinters is 10.2 seconds, so the time after reaching maximum speed is 10.2 - 2 = 8.2 seconds.

Since sprinter A is running at maximum speed for the remainder of the race, the final velocity is the same as the maximum speed. Let's denote the maximum speed as v_max.

acceleration_A = (v_max - 0) / 2
= v_max / 2

Sprinter B:
Sprinter B took 3 seconds to reach maximum speed. Using the same logic as before, the time after reaching maximum speed is 10.2 - 3 = 7.2 seconds.

acceleration_B = (v_max - 0) / 3
= v_max / 3

Therefore, the acceleration for sprinter A is v_max / 2, and the acceleration for sprinter B is v_max / 3.