Final answer:
To determine the sprinter's total race time, we must first calculate the time taken to accelerate for the first 40 meters and then find the sprinter's final velocity. This velocity is maintained for the remaining distance and allows us to calculate the remaining time, summing both to get the total time.
Step-by-step explanation:
The student's question is about calculating the time taken by a 64.0 kg sprinter to complete a 100 m dash given that the sprinter starts with a constant acceleration over a certain distance and then maintains the resulting velocity for the rest of the race. This involves concepts from kinematics in physics.
First, we need to find the time it takes for the sprinter to accelerate over the first 40 meters. The kinematic equation we use for this is:
s = ut + ½at2
Where s is the distance traveled, u is the initial velocity (which is 0 m/s for a standing start), a is the acceleration (2.24 m/s2), and t is the time. Plugging in the numbers and solving for t gives us the time to cover the first 40 meters.
Next, we calculate the velocity at the end of 40 meters using the equation:
v = u + at
Using the previously found time, we can find the velocity the sprinter has after 40 meters. Since the sprinter maintains this velocity for the remaining 60 meters, we calculate the time for this part by dividing the remaining distance by this constant velocity. Summing both times gives us the total time for the 100 m dash.