University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
Textbook Question
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Chapter 4, Problem 4.1CYU

Chapter 4, Problem 4.1CYU,

Expert Solution
Check Mark
To determine

(a)

The instantaneous velocity at t = 3 s. if the position function of a particle is:

r(t)=3t3i^+4j^

Answer to Problem 4.1CYU

The instantaneous velocity at t = 3 s will be (81ms)i^

Explanation of Solution

Given info:

r(t)=3t3i^+4j^

Formula used:

The instantaneous velocity is given by

v(t)=dr(t)dt

Calculation:

Substituting the values in above formula, we get

v(t)=9t2i^+0At,t=3sv(3s)=9(3)2i^=(81ms)i^

Thus, instantaneous velocity at t= 3 s will be (81ms)i^ for the given position function.

Expert Solution
Check Mark
To determine

(b)

If the average velocity between 2s and 4s is equal to the instantaneous velocity at t= 3s

Answer to Problem 4.1CYU

The average velocity between t = 2 s and t = 4 s is (84ms)i^ which is not equal to the instantaneous velocity at t = 3 s.

Explanation of Solution

Given info:

r(t)=3t3i^+4j^

Formula used:

The average velocity is given by:

vave=r(4)r(2)t(4)t(2)

Calculation:

r(t)=3t3i^+4j^r(2s)=3(2)3i^+4j^=24i^+4j^ r(4s)=3(4)3i^+4j^=192i^+4j^

Then the average velocity is:

r(t)=3t3i^+4j^r(2s)=3(2)3i^+4j^=24i^+4j^ r(4s)=3(4)3i^+4j^=192i^+4j^v¯=r(4s)r(2s)t(4s)t(2s)=(192i^+4j^)m(24i^+4j^)m4s2sv¯=(168m)i^2s=(84ms)i^

Thus, the average velocity between t = 2 s and t = 4 s is (84ms)i^ which is not equal to the instantaneous velocity at t = 3 s.

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Chapter 4 Solutions

University Physics Volume 1

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