Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A muon (an elementary particle) enters a region with a speed of $5.00 \times 10^{6} m / s$ and then is slowed down at the rate of $1.25 \times 10^{14} m / s^{2}$ . (a) How far does the muon take to stop? (b) Graph x vs t and v vs t for the muon.

(a) The distance muon takes to stop is 0.100 m .

(b) The graphs of x vs t and v vs tare plotted for the muon.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

Initial speed of muon is, $v_{i} = 5.00 \times 10^{6} m / s$

Acceleration of the muon is, $a = - 1.25 \times 10^{14} m / s^{2}$

Step 2: Understanding the kinematic equations of motion.

Kinematic equations of motion describe the relationship between displacement, velocity or acceleration of a particle. The graphs of displacement vs time and velocity vs timecan be plotted to analyze the motion of the particle.

The expression for the equation of motion is given as below,

$v_{f}^{2} = v_{i}^{2} + 2 a x$ (i)

Here, $v_{f}$ is the final velocity, $v_{i}$ is the initial velocity, $a$ is the acceleration, and $x$ is the distance.

Step3: (a) Determination of the distance required for muon to stop

Rearrange the equation (i) for x and substitute the values.

$x = \frac{v_{f}^{2} - v_{i}^{2}}{2 a} = \frac{(0^{2} - {(5.00 \times 10^{6})}^{2})}{(2 \times (- 1.25) \times 10^{14})} = 0.100 m$

Step 4: (b) Plotting the graph of x vs t and v vs t.

To plot graph of vs kinematic equationis used,

$x = v_{i} t + \frac{1}{2} a t^{2} x = (5.00 \times 10^{6} \times t) + (\frac{1}{2} \times (- 1.25 \times 10^{14} \times t^{2}))$

To plot graph of vs t kinematic equation is used,

$v = v_{i} + a t v = (5.00 \times 10^{6}) + (- 1.25 \times 10^{14} \times t)$

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Fundamentals Of Physics

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Short Answer

A muon (an elementary particle) enters a region with a speed of $5.00 \times 10^{6} m / s$ and then is slowed down at the rate of $1.25 \times 10^{14} m / s^{2}$ . (a) How far does the muon take to stop? (b) Graph x vs t and v vs t for the muon.

Step by Step Solution

Step 1: Given Data

Step 2: Understanding the kinematic equations of motion.

Step3: (a) Determination of the distance required for muon to stop

Step 4: (b) Plotting the graph of x vs t and v vs t.

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Fundamentals Of Physics

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Short Answer

A muon (an elementary particle) enters a region with a speed of 5.00×106 m/s and then is slowed down at the rate of 1.25×1014 m/s2. (a) How far does the muon take to stop? (b) Graph x vs t and v vs t for the muon.

Step by Step Solution

Step 1: Given Data

Step 2: Understanding the kinematic equations of motion.

Step3: (a) Determination of the distance required for muon to stop

Step 4: (b) Plotting the graph of x vs t and v vs t.

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A muon (an elementary particle) enters a region with a speed of $5.00 \times 10^{6} m / s$ and then is slowed down at the rate of $1.25 \times 10^{14} m / s^{2}$ . (a) How far does the muon take to stop? (b) Graph x vs t and v vs t for the muon.