Question

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?

Answer 1

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