Kinematics Problem (please help me)

Question

In a 100m race, a sprinter accelerates for the first 40.0m at 2.56 m/s (squared). After this distance he reaches top speed and maintains this speed for the rest of the race. How long does it take him to run the entire race?

Answer 1

For the first 40 meter, assuming the sprinter starts from rest, we can use the kinematic equation:

x = 1/2at² to find the time during that portion of the race:

40 = 1/2(2.56)t²

80 = (2.56)t²

31.25 = t²

t = 5.59017 s

To find his speed after that period of time, we can use V = at = (2.56)(5.59017) = 14.3108 m/s

The sprinter runs for 60 m at that speed so the time running on this portion of the race is distance/speed = 60/14.3108 = 4.19263 s

Total time is 5.59017 + 4.19263 = 9.78 seconds