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Q26P

Expert-verifiedFound in: Page 34

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**A muon (an elementary particle) enters a region with a speed of ${\mathbf{5}}{\mathbf{.}}{\mathbf{00}}{\mathbf{\times}}{{\mathbf{10}}}^{{\mathbf{6}}}{\mathbf{}}{\mathbf{m}}{\mathbf{/}}{\mathbf{s}}$**** and then is slowed down at the rate of ${\mathbf{1}}{\mathbf{.}}{\mathbf{25}}{\mathbf{\times}}{{\mathbf{10}}}^{{\mathbf{14}}}{\mathbf{}}{\mathbf{m}}{\mathbf{/}}{{\mathbf{s}}}^{{\mathbf{2}}}$****. (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 *t*are plotted for the muon.

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

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

**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,

${v}_{f}^{2}={v}_{i}^{2}+2ax$(i)

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

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

$x=\frac{{v}_{f}^{2}-{v}_{i}^{2}}{2a}\phantom{\rule{0ex}{0ex}}=\frac{\left({0}^{2}-{\left(5.00\times {10}^{6}\right)}^{2}\right)}{\left(2\times \left(-1.25\right)\times {10}^{14}\right)}\phantom{\rule{0ex}{0ex}}=0.100\mathrm{m}$

To plot graph of vs kinematic equationis used,

$x={v}_{i}t+\frac{1}{2}a{t}^{2}\phantom{\rule{0ex}{0ex}}x=\left(5.00\times {10}^{6}\times t\right)+\left(\frac{1}{2}\times \left(-1.25\times {10}^{14}\times {t}^{2}\right)\right)$

To plot graph of vs *t* kinematic equation is used,

$v={v}_{i}+at\phantom{\rule{0ex}{0ex}}v=\left(5.00\times {10}^{6}\right)+\left(-1.25\times {10}^{14}\times t\right)$

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