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 0.550 m/s^{2} for 7.00 s.

(a) What is his final velocity? m/s (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? s (c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 12.7 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish? distance m time s

Thank you for the opportunity to help you with your question!

a) V1 = Vo + a*t =12.5 + 0.550*7 =
16.35
m/s distance = 12.5*7 + 0.275*7^2 = 100.975 m.
b) d = V1*T2 = 300-100.975 =
199.025
16.35*T2 = 199.025
T2 =
12.17278
s
T1+T2 = 7 + 12.17278 =
19.17278
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 - 19.17278 =
4.82722
s Saved.

I will post the last part soon

Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 8th, 2015

Part c

d = V*T = 300-5 = 295 m.
12.7 * T = 295.
T =
23.22835
s. To finish.

23.22835
- 19.17278=
4.05557
s. Behind the winner.

300m/19.17278s * 4.05557s. =
63.46
m. Behind the
winner.

Let me see, How I made it wrong. I guess its because such kind of questions come with a short time of 20 minutes thus the pressure can cause one to do a mistake.

You know I was shocked to hear that A was wrong. I even felt like giving up on doing them. Let me go through C and see what value I have done wrongly.. Thanks

d = V*T = 300-5 = 295 m.
12.7 * T = 295.
T =
23.22835
s. To finish.

23.22835
- 19.17278=
4.05557
s. Ahead

In Meters time traveled at finish of winner =19.17278s D = s x time =12.5 x 19.17278 =
239.6598
m subtract it from the total distance of 295 =295-
239.6598
=
55.3402

I had plugged in the figure for the winner instead of for the guy in position 2 300m/19.17278s * 4.05557s. =
63.46
m. Behind the
winner.