A cyclist sprints at the end of a race to clinch a victory....

A cyclist sprints at the end of a race to clinch a victory. She has an initial velocity of $11.5 \mathrm{m} / \mathrm{s}$ and accelerates at a rate of $0.500 \mathrm{m} / \mathrm{s}^{2}$ for $7.00 \mathrm{s}$. (a) What is her final velocity? (b) The cyclist continues at this velocity to the finish line. If she is 300 m from the finish line when she starts to accelerate, how much time did she save? (c) The second-place winner was $5.00 \mathrm{m}$ ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at $11.8 \mathrm{m} / \mathrm{s}$ until the finish line. What was the difference in finish time in seconds between the winner and runner-up? How far back was the runner-up when the winner crossed the finish line?

Key Concepts

Relative Motion

This concept involves comparing the motions of two or more objects. It is used to analyze differences in position, speed, or time when objects are moving simultaneously but under different conditions, facilitating the determination of leads, lags, or time differences between them.

Kinematic Equations

These are the fundamental equations used to analyze the motion of objects under constant acceleration. They include formulas such as v = u + at and s = ut + ½at², which enable the calculation of parameters like displacement, velocity, and time during different phases of motion.

Constant Velocity

This is the type of motion in which an object moves with a steady speed in a given direction, implying zero acceleration. The distance covered is directly proportional to the time taken, and it simplifies calculations once acceleration ceases.

Uniform Acceleration

This concept deals with motion where the velocity of an object increases or decreases at a constant rate over time. It is characterized by a constant acceleration, and the motion is analyzed using equations that relate initial velocity, final velocity, acceleration, time, and displacement.

Transcript

00:01 We are considering a cyclist who sprints at the end of a race.

00:05 If her initial velocity is 11 .5 meters per seconds, and she accelerates at an acceleration rate of 0 .50 meters per second squared for seven seconds, what is her final velocity? okay, so our final velocity will equal our initial velocity plus at.

00:33 So my final velocity will equal 11 .5 plus 0 .5 .00.

00:59 And this will be 3 .5.

01:04 That'll be 50 meters per second.

01:13 If she continues this, continues this velocity to the finish time.

01:23 How much time will she say? is she's 300 meters from the finish line when she starts to accelerate? okay, so if she was going to time at 11 .5 seconds or meters per second would have been 11 .5 meters per second.

02:02 And we're going to, i've got to figure this out the other way around here.

02:07 This would be 300 meters times one second and 11 .5 meters.

02:21 That's 2 .6 .1 times 10 to the first.

02:25 First 26 .1 seconds.

02:31 Okay, but she's accelerating and she reaches the final velocity.

02:39 Let's go to the next page.

02:45 Distance covered while accelerating.

03:06 Okay, that'll be, so x1 will equal 11 .5 times seven seconds plus 0 .5 times 0 .50 meters per second squared times 7 squared.

03:48 Okay, 11 .5 times minus, parentheses, 0 .5 times .5 times 49.

04:01 And i get, i forgot to, and i get 68 .25 meters.

04:31 That is, i'm just checking my math.

04:54 5 times, 0 .5 times.