#### A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.5 m/s and accelerates at the rate of 0.500 m/s^{2} 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 11.8 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

**Solution:**

### Part A

### Part B

Let *t _{const}* be the time it takes to reach the finish line without accelerating:

Now let *d *be the distance traveled during the 7 seconds of acceleration. We know *t=7.00 s* so

Let *t’ *be the time it will take the rider at the constant final velocity to complete the race:

So the total time *T *it will take the accelerating rider to reach the finish line is

Finally, let T^{*} be the time saved. So

### Part C

Let t_{2} be the time it takes for rider 2 to reach the finish line.

The time difference is

Therefore, he finishes 4.2 s after the winner.

When the other racer reaches the finish line, the winner has been traveling at 15 m/s for 4.2 seconds, so the other racer finishes

behind the other racer.