During a ski race, Kate uniformly accelerated at 3.15m/s^2 for 100meters. She then maintained this velocity for another 100m. she then uniformly decelerated at 6m/s^2 for 2 seconds. she accelerates back to her maximum velocity over the next 200meters in 16 seconds. she then travleled 1.0km at this maximum velocity

what was her maximum velocity and what distance did she travel while decelerating at 6.00m/s^2

To find Kate's maximum velocity, we will consider her acceleration and the distances she traveled.

1. In the first part of the race, Kate uniformly accelerated at 3.15 m/s^2 for 100 meters. We can use the equation of motion to find her final velocity (v) after this acceleration:
v^2 = u^2 + 2as
where u is the initial velocity, a is the acceleration, and s is the distance.
Assuming Kate started from rest (u = 0), we have:
v^2 = 0^2 + 2 * 3.15 * 100
v^2 = 630
v = √630
v ≈ 25.12 m/s

2. Kate then maintained this velocity for another 100 meters. Since there is no acceleration, her final velocity remains the same at 25.12 m/s.

3. Next, Kate uniformly decelerated at 6 m/s^2 for 2 seconds. Here, we will use the equation of motion:
v = u + at
where u is the initial velocity, a is the acceleration, t is the time, and v is the final velocity.
We know the deceleration (a), the time (t), and the initial velocity (25.12 m/s).
We need to calculate the final velocity:
v = 25.12 - 6 * 2
v ≈ 13.12 m/s

4. After decelerating, Kate accelerates back to her maximum velocity over the next 200 meters in 16 seconds. We will use the equation:
v = u + at
We know the acceleration (a), the time (t), and the initial velocity (13.12 m/s) to find the final velocity:
v = 13.12 + 3.15 * 16
v ≈ 61.12 m/s

5. Finally, Kate traveled 1.0 kilometer (1000 meters) at her maximum velocity. Therefore, the distance covered while decelerating at 6.00 m/s^2 would be:
Total distance - Distance accelerated - Distance maintained - Distance accelerated again
1000 - 100 - 100 - 200 = 600 meters

So, Kate's maximum velocity is approximately 61.12 m/s, and she traveled a distance of 600 meters while decelerating at 6.00 m/s^2.