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: A ball dropped from a state of rest at time t = 0 travels a distance s ( t ) = 4.9 t 2 m in t seconds. A table is given to compute the average velocity at different time intervals. Interval [ 2 , 2.01 ] [ 2 , 2.005 ] [ 2 , 2.001 ] [ 2 , 2.00001 ] Average Velocity Formula Used: a. The distance travelled by the ball during the time interval [ t 0 , t 1 ] is Δ s = s ( t 1 ) − s ( t 0 ) b. 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. The distance travelled by the ball in t seconds is given: s ( t ) = 4.9 t 2 The distance travelled by the ball during the time interval [ 2 , 2.5 ] is Δ s = s ( t 1 ) − s ( t 0 ) = s ( 2.5 ) − s ( 2 ) = 4.9 ( 2.5 ) 2 − 4.9 ( 2 ) 2 = 11.025 m Thus, the distance travelled by the ball during the time interval [ 2 , 2.5 ] is 11.025 m . b. The average velocity over [ 2 , 2.5 ] is Δ s Δ t = s ( t 1 ) − s ( t 0 ) t 1 − t 0 = s ( 2.5 ) 2 − s ( 2 ) 2 2.5 − 2 = 11.025 0.5 = 22.05 m / s Thus, The average velocity over [ 2 , 2.5 ] is 22.05 m / s . c. Time interval is given in the table according to that compute average velocity. • The average velocity over [ 2 , 2.01 ] is Δ s Δ t = s ( 2.01 ) − s ( 2 ) 2.01 − 2 = 4.9 ( 2.01 ) 2 − 4.9 ( 2 ) 2 0.01 = 19.649 m / s Thus, the average velocity for the time interval [ 2 , 2.01 ] is 19.649 m / s . • The average velocity over [ 2 , 2.005 ] is Δ s Δ t = s ( 2.005 ) − s ( 2 ) 2

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 2.1, Problem 1E

To determine

a. The distance the ball travels during the time interval [2,2.5]

b. The average velocity over [2,2.5]

c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t=2.

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Chapter 2.1, Problem 4PQ

Chapter 2.1, Problem 2E

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Chapter 2 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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a. The distance the ball travels during the time interval [ 2 , 2.5 ] b. The average velocity over [ 2 , 2.5 ] c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t = 2 .

Solution Summary: The author explains that the average velocity does not describe the motion of the particular instant of time, so to know how fast the particle moves, we define the instantaneous velocity.

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a. The distance the ball travels during the time interval [2,2.5]

b. The average velocity over [2,2.5]

c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t=2.

Want to see the full answer?

Chapter 2 Solutions

a. The distance the ball travels during the time interval [ 2 , 2.5 ] b. The average velocity over [ 2 , 2.5 ] c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t = 2 .

Solution Summary: The author explains that the average velocity does not describe the motion of the particular instant of time, so to know how fast the particle moves, we define the instantaneous velocity.

Concept explainers

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a. The distance the ball travels during the time interval [2,2.5] b. The average velocity over [2,2.5] c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t=2.

Want to see the full answer?

Chapter 2 Solutions

a. The distance the ball travels during the time interval [2,2.5]

b. The average velocity over [2,2.5]

c. The average velocity for the time intervals in the table and the ball’s instantaneous velocity at t=2.