Explanation The average velocity does not describe the motion of the particular instant of time during which time interval the average velocity is calculated. Hence, to know how fast the particle moves at a particular instant of time, we define the instantaneous velocity. Given: The height of a projectile fired in the air vertically with initial velocity 25 m / s is: h ( t ) = 25 t − 4.9 t 2 m . Formula Used: The average velocity over [ t 0 , t 1 ] is Δ s Δ t = s ( t 1 ) − s ( t 0 ) t 1 − t 0 Calculation: a. h ( t ) = 25 t − 4.9 t 2 m so, h ( 1 ) is: h ( 1 ) = 25 ( 1 ) − 4.9 ( 1 ) 2 = 25 − 4.9 = 20.1 Thus, h ( 1 ) = 20.1 Now compute h ( t ) − h ( 1 ) factored with ( t − 1 ) as a factor: h ( t ) − h ( 1 ) = 25 t − 4.9 t 2 − ( 25 ( 1 ) − 4.9 ( 1 ) 2 ) = 25 ( t − 1 ) − 4.9 ( t 2 − 1 ) = 25 ( t − 1 ) − 4.9 ( t − 1 ) ( t + 1 ) = ( t − 1 ) ( 20.1 − 4.9 t ) Thus, h ( t ) − h ( 1 ) can be factored with ( t − 1 ) as a factor: ( t − 1 ) ( 20.1 − 4.9 t ) b

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 2.1, Problem 26E

To determine

a. The value of h(1) and show that h(t)−h(1) can be factored with (t−1) as a factor.

b. By using part (a), show that the average velocity over the interval [1,t] is 20.1−4.9t

c. By using this formula, find the average velocity over several intervals [1,t] with t close to 1. Then estimate the instantaneous velocity at time t=1

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Chapter 2.1, Problem 25E

Chapter 2.1, Problem 27E

Chapter 2 Solutions

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Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

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Solution Summary: The author explains that the average velocity does not describe the motion of the particular instant of time during which the instantaneous velocity is calculated.

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