Sprinter Usain Bolt reached a maximum speed of 11.2 m / s in 2.0 s while running the 100-m das

step 1 All right, crushing 49. Sprinter use a safe bolt reached a maximum speed of 11 .2 meters per sec

Sprinter Usain Bolt reached a maximum speed of 11.2 m / s...

Sprinter Usain Bolt reached a maximum speed of $11.2 \mathrm{~m} / \mathrm{s}$ in $2.0 \mathrm{~s}$ while running the $100-\mathrm{m}$ dash. (a) What was his acceleration? (b) What distance did he travel during this first $2.0 \mathrm{~s}$ of the race? (c) What assumptions did you make? (d) What time interval was needed to complete the race, assuming that he ran the last part of the race at his maximum speed? (e) What is the total time for the race? How certain are you of the number you calculated?

Sprinter Usain Bolt reached a maximum speed of $11.2 \mathrm{~m} / \mathrm{s}$ in $2.0 \mathrm{~s}$ while running the $100-\mathrm{m}$ dash. (a) What was his acceleration? (b) What distance did he travel during this first $2.0 \mathrm{~s}$ of the race? (c) What assumptions did you make?
(d) What time interval was needed to complete the race, assuming that he ran the last part of the race at his maximum speed? (e) What is the total time for the race? How certain are you of the number you calculated?

Key Concepts

Acceleration

Acceleration is the rate of change of velocity over time. It is a fundamental concept in kinematics that describes how quickly an object speeds up or slows down, and is calculated using the relation a = ?v/?t. This concept is essential for understanding motion in any context where speed changes over time.

Uniformly Accelerated Motion

Uniformly accelerated motion refers to movement where the acceleration remains constant over time. This scenario allows for the application of standard kinematic equations, such as v = at and x = ½at², which are used to compute velocity and distance covered during the acceleration phase.

Constant Velocity Motion

Constant velocity motion describes movement at an unchanging speed. When an object moves with constant velocity, its distance traveled can be calculated by the equation x = vt. This concept is particularly important when analyzing segments of motion where acceleration is zero.

Segmented Motion Analysis

Segmented motion analysis involves breaking down a complex motion into different parts—typically an acceleration phase followed by a phase of constant velocity. This approach allows for the application of specific kinematic equations to each segment, and the overall motion is understood by summing the contributions from each phase.

Assumptions in Kinematics Problems

Assumptions are made in kinematics to simplify the analysis of motion, such as considering acceleration to be constant or neglecting external factors like air resistance. Recognizing these assumptions is critical to understanding the limitations and approximations inherent in the calculated results.

Transcript

00:01 All right, crushing 49.

00:04 Sprinter use a safe bolt reached a maximum speed of 11 .2 meters per second in two seconds while running the 100 meter dash.

00:12 A, what was his acceleration? i'll do the rest later, actually.

00:17 So we'll just go question by question here.

00:20 Part a asks, what is his acceleration? so i think it's safe enough to assume that i've seen a sprinting race, you are held at the start, and then the gun goes off and you start.

00:32 So i think it's safe to say that our initial velocity here can be considered to be zero.

00:37 Initial velocity is zero meters per second because you're just waiting before you go.

00:42 If that's the case, we can use the expression that the velocity equals the initial velocity plus acceleration in time to time.

00:50 We can ignore this initial velocity and determine that acceleration is simply velocity over time.

00:57 And since this final velocity is 11 .2 meters per second, over two seconds.

01:06 Using bolt's acceleration, average acceleration in this time frame, simply 5 .6 meters per second squared to two significant digits, of course, because that's what we start with.

01:21 Okay, b, what distance did he travel during the first two seconds of the race? so the two seconds is the time it takes to accelerate, so we can find for part b that the distance he travels.

01:37 Is again the kinmanac expression, initial velocity times time, plus one half a t squared.

01:46 Again, very safe to assume the initial velocity is zero, one half times 5 .6 times two seconds squared, results in a distance of 11 .2 meters.

02:06 Part c, what assumptions did you make? well, the one that we stated initially is that the initial speed is zero.

02:12 Meters per second.

02:14 We can say he moves in a straight line, uniform acceleration throughout the race.

02:20 Nothing in his way.

02:21 So he is running fully straight without going up or down.

02:25 I guess hard to go down, without like jumping or going too high out of that linear motion.

02:29 So anything like that would be appropriate responses for that part of the question.

02:36 Part d.

02:38 What time interval was needed to complete the race, assuming that he ran the last part of the race at his maximum speed...

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