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Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 02: Motion Along a Straight LineProblema 16
Capitolo 2, Problema 16

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 1010-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right.
(a) At the beginning of the interval, the astronaut is moving toward the right along the xx-axis at 15.015.0 m/s, and at the end of the interval she is moving toward the right at 5.05.0 m/s.
(b) At the beginning she is moving toward the left at 5.05.0 m/s, and at the end she is moving toward the left at 15.015.0 m/s.
(c) At the beginning she is moving toward the right at 15.015.0 m/s, and at the end she is moving toward the left at 15.015.0 m/s.

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To find the average acceleration, use the formula: \( a_{avg} = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time interval.
For interval (a), calculate \( \Delta v \) as the final velocity minus the initial velocity: \( \Delta v = 5.0 \text{ m/s} - 15.0 \text{ m/s} = -10.0 \text{ m/s} \). The time interval \( \Delta t \) is 10 s.
Substitute \( \Delta v = -10.0 \text{ m/s} \) and \( \Delta t = 10 \text{ s} \) into the average acceleration formula: \( a_{avg} = \frac{-10.0 \text{ m/s}}{10 \text{ s}} \). The negative sign indicates the acceleration is to the left.
For interval (b), calculate \( \Delta v \) as the final velocity minus the initial velocity: \( \Delta v = -15.0 \text{ m/s} - (-5.0 \text{ m/s}) = -10.0 \text{ m/s} \). The time interval \( \Delta t \) is 10 s.
Substitute \( \Delta v = -10.0 \text{ m/s} \) and \( \Delta t = 10 \text{ s} \) into the average acceleration formula: \( a_{avg} = \frac{-10.0 \text{ m/s}}{10 \text{ s}} \). The negative sign indicates the acceleration is to the left.

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Concetti chiave

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Average Acceleration

Average acceleration is defined as the change in velocity divided by the time over which the change occurs. It is a vector quantity, meaning it has both magnitude and direction. The formula is a_avg = (v_final - v_initial) / Δt, where v_final is the final velocity, v_initial is the initial velocity, and Δt is the time interval.
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Solving Constant and Average Velocity Problems

Velocity and Direction

Velocity is a vector quantity that describes the speed of an object in a specific direction. In this problem, the direction is along the x-axis, with positive values indicating movement to the right and negative values indicating movement to the left. Understanding the direction is crucial for determining the sign of the velocity and acceleration.
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Sign Convention

In physics, sign convention is used to indicate direction. For this problem, the positive direction is defined as to the right. Therefore, a positive velocity or acceleration indicates movement or acceleration to the right, while a negative value indicates movement or acceleration to the left. This helps in determining the algebraic sign of the average acceleration.
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