Question

If the sprinter accelerates at that rate for 20.00 m and then maintains that velocity for the remainder of a 100.00-m dash, what will her time be for the race?

a) 8.00 s
b) 9.52 s
c) 8.94 s
d) 9.25 s

Answer 1

The sprinter's time for the race is 9.81 seconds.

Step-by-step explanation:

To find the sprinter's time for the race, we need to divide the race into two parts: the acceleration phase and the constant velocity phase. Let's start with the acceleration phase:

1. In the acceleration phase, the sprinter accelerates at a rate of 4.50 m/s² for 20.00 m.
2. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can find the final velocity at the end of the acceleration phase: v = 0 + 4.50 m/s² * 2.40 s = 10.80 m/s.

Now, let's move on to the constant velocity phase:

1. In the constant velocity phase, the sprinter maintains a constant velocity of 10.80 m/s for the remaining distance of 100.00 m - 20.00 m = 80.00 m.
2. Using the equation v = d/t, where v is the velocity, d is the distance, and t is the time, we can find the time for the constant velocity phase: t = d/v = 80.00 m / 10.80 m/s = 7.41 s.

To find the total time for the race, we add the time for the acceleration phase and the time for the constant velocity phase: 2.40 s + 7.41 s = 9.81 s.