Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

An electron with an initial velocity $V_{0} = 1.50 \times 10^{5} m / s$ enters a region of length L=1.00cm where it is electrically accelerated. It emerges with $v = 5.70 \times 10^{6} m / s$ . What is its acceleration, assumed constant?

The acceleration of electron to be assumed constant is $1.62 \times 10^{15} m / s^{2}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

Initial velocity, $v_{0} = 1.50 \times 10^{5} m / s$

Final velocity, $v = 5.70 \times 10^{5} m / s$

Distance travelled, x=1.00 cm

Step 2: Understanding the concept of acceleration

Acceleration can be found by using the given data in the kinematic equation which involves initial velocity, final velocity, acceleration, and displacement terms.

The formula to find acceleration can be obtained with the help of final as well as initial velocity.

$v^{2} = v_{0}^{2} + 2 a x Here, v is the final velocity, v_{0} is the initial velocity, a is the acceleration and x is the distance travelled .$

Step 3: Determination of the acceleration.

Convert 1.00 cm into i.e. in S.I. units.

$1 cm = \frac{1 cm}{100 cm} \times 1 m = 0.01 m Rearrange the equation (i) to calculate the acceleration as, a = \frac{v^{2} - v_{0}^{2}}{2 x} Substitute the values in the above expression . a = \frac{{(5.7 \times 10^{6} m / s)}^{2} - {(1.5 \times 10^{5} m / s)}^{2}}{2 \times 0.01 m} = 1.62 \times 10^{15} m / s^{2} Therefore, the acceleration of the electron to be assumed constant is 1.62 \times 10^{15} m / s^{2} .$

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Fundamentals Of Physics

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Short Answer

An electron with an initial velocity $V_{0} = 1.50 \times 10^{5} m / s$ enters a region of length L=1.00cm where it is electrically accelerated. It emerges with $v = 5.70 \times 10^{6} m / s$ . What is its acceleration, assumed constant?

Step by Step Solution

Step 1: Given Data

Step 2: Understanding the concept of acceleration

Step 3: Determination of the acceleration.

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An electron with an initial velocityV0=1.50×105 m/senters a region of length L=1.00cm where it is electrically accelerated. It emerges withv=5.70×106m/s. What is its acceleration, assumed constant?

Step by Step Solution

Step 1: Given Data

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An electron with an initial velocity $V_{0} = 1.50 \times 10^{5} m / s$ enters a region of length L=1.00cm where it is electrically accelerated. It emerges with $v = 5.70 \times 10^{6} m / s$ . What is its acceleration, assumed constant?