A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 12.5 m/s and accelerates at the rate of 0.450 m/s2 for 7.00 s.

(a) What is his final velocity?

(b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when he started to accelerate, how much time did he save?

(c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 12.8 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?
distance

a. V1 = Vo + a*t=12.5 + 0.450*7=15.7m/s.

d1 = 12.5*7 + 0.225*7^2 = 98.5 m.

b. d2 = V1*T2 = 300-98.5 = 201.5
15.7*T2 = 201.5
T2 = 12.8 s.
T1+T2 = 7 + 12.8 = 19.8 s. To travel 300 m with acceleration.

d = Vo*T3 = 300 m.
12.5*T3 = 300.
T3 = 24 s. To travel 300 m without accelerating.

T = T3-(T1+T2) = 24 - 19.8 = 4.2s Saved.

c. d = V*T = 300-5 = 295 m.
12.8 * T = 295.
T = 23 s. To finish.

23 - 19.8 = 3.2 s. Behind the winner.

300m/19.8s * 3.2s. = 48.5 m. Behind the
winner.

THIS IS A CORRECTION FOR PART C, WHEN YOU ARE SUPPOSED TO CONVERT SECONDS TO METERS!!! THE REST IS CORRECT THOUGH.

c.

12.8 m/s * 3.2s = 40.96 (NOT 48.5)

woops nvm, I was looking at another problem.

Actually Jasmine was correct on her Correction. the answer for c. os 40.96m

To solve these problems, we can use the equations of motion for uniformly accelerated motion. The relevant equations are:

1. Final velocity (v) = Initial velocity (u) + (Acceleration (a) * Time (t))
2. Distance (s) = Initial velocity (u) * Time (t) + (0.5 * Acceleration (a) * Time (t)^2)

(a) To find the final velocity of the racer, we can use Equation 1. Given:
Initial velocity (u) = 12.5 m/s
Acceleration (a) = 0.450 m/s^2
Time (t) = 7.00 s

Using Equation 1:
Final velocity (v) = 12.5 m/s + (0.450 m/s^2 * 7.00 s)
Final velocity (v) = 12.5 m/s + 3.15 m/s
Final velocity (v) = 15.65 m/s

Therefore, the final velocity of the racer is 15.65 m/s.

(b) To find the time saved by the racer, we need to calculate the time it would have taken to cover the 300 m at the initial velocity before accelerating. We can use Equation 2. Given:
Initial velocity (u) = 12.5 m/s
Acceleration (a) = 0 m/s^2 (because the racer didn't accelerate)
Distance (s) = 300 m

Using Equation 2:
Distance (s) = 12.5 m/s * Time (t) + (0.5 * 0 m/s^2 * Time (t)^2)
300 m = 12.5 m/s * Time (t)

Solving for Time (t):
Time (t) = 300 m / 12.5 m/s
Time (t) = 24 s

The time it would have taken to cover 300 m at the initial velocity is 24 s.

The racer accelerated for 7 s, so the time saved is:
Time saved = Time taken (without acceleration) - Time taken (with acceleration)
Time saved = 24 s - 7 s
Time saved = 17 s

Therefore, the racer saved 17 seconds.

(c) To find how far ahead of the other racer the winner finished, we need to calculate the distance covered by both racers. For the other racer, who traveled at a constant velocity:
Velocity (v) = 12.8 m/s
Time (t) = 7 s (because both racers started accelerating at the same time)

Using Equation 2 for the other racer:
Distance (s) = 12.8 m/s * 7 s
Distance (s) = 89.6 m

The other racer covered a distance of 89.6 m.

The winner traveled 300 m to the finish line, so the distance they finished ahead of the other racer is:
Distance ahead = Distance (winner) - Distance (other racer)
Distance ahead = 300 m - 89.6 m
Distance ahead = 210.4 m

Therefore, the winner finished 210.4 meters ahead of the other racer.