Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
1st Edition
ISBN: 9781305259836
Author: Debora M. Katz
Publisher: Cengage Learning
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Chapter 4, Problem 77PQ

(a)

To determine

Find the velocity of the particle as a function of time.

(a)

Expert Solution
Check Mark

Answer to Problem 77PQ

The velocity of the particle as a function of time is (2.00+233t3/2)i^+(7.00t22)j^.

Explanation of Solution

Write the equation for velocity.

    ifdv=ifadt=Δvifadt=vvi                                                             (I)

Here, a is the time in acceleration, v is the velocity and vi is the initial velocity.

Conclusion:

Substitute (2.00i^+7.00j^) m/s for vi and (3t1/2i^tj^) m/s2 for a in equation I.

    0t((3t1/2i^tj^) m/s2)dt=v((2.00i^+7.00j^) m/s)v=(2.00i^+7.00j^) m/s+0t3t1/2i^dt0ttj^dt=(2.00i^+7.00j^) m/s+[3t3/23/2]0ti^[t22]0tj^=(2.00+233t3/2)i^+(7.00t22)j^

Therefore, the velocity of the particle as a function of time is (2.00+233t3/2)i^+(7.00t22)j^.

(b)

To determine

Find the position of the particle as a function of time.

(b)

Expert Solution
Check Mark

Answer to Problem 77PQ

The position of the particle as a function of time is (2.00t+4315t5/2)i^+(7.00tt36)j^.

Explanation of Solution

Write the equation for position.

    ifdr=ifvdt=Δrifvdt=rri                                                             (II)

Here, ri is the initial position.

Conclusion:

Substitute 0 for ri and (2.00+233t3/2)i^+(7.00t22)j^ for v in equation II.

    if((2.00+233t3/2)i^+(7.00t22)j^)dt=r0r=0t(2.00+233t3/2)i^dt0t(7.00t22)j^dt=(2.00t+4315t5/2)i^+(7.00tt36)j^

Therefore, the position of the particle as a function of time is (2.00t+4315t5/2)i^+(7.00tt36)j^.

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Chapter 4 Solutions

Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics

Ch. 4 - A basketball player dribbles the ball while...Ch. 4 - A motion diagram of a bouncing ball is shown in...Ch. 4 - Prob. 6PQCh. 4 - Prob. 7PQCh. 4 - Figure P4.8 shows the motion diagram of two balls,...Ch. 4 - Prob. 9PQCh. 4 - Prob. 10PQCh. 4 - Prob. 11PQCh. 4 - If a particles speed is always increasing, what...Ch. 4 - Prob. 13PQCh. 4 - An aircraft flies at constant altitude (with...Ch. 4 - A glider is initially moving at a constant height...Ch. 4 - If the vector components of the position of a...Ch. 4 - A If the vector components of a particles position...Ch. 4 - Prob. 18PQCh. 4 - A The spiral is an example of a mathematical form...Ch. 4 - A circus performer stands on a platform and throws...Ch. 4 - Anthony carelessly rolls his toy car off a...Ch. 4 - A physics student stands on a second-story balcony...Ch. 4 - During the battle of Bunker Hill, Colonel William...Ch. 4 - A During the battle of Bunker Hill, Colonel...Ch. 4 - A softball is hit with an initial velocity of 29.0...Ch. 4 - Figure P4.8 shows the motion diagram of two balls....Ch. 4 - A circus performer throws an apple toward a hoop...Ch. 4 - An arrow is fired with initial velocity v0 at an...Ch. 4 - A rock is thrown horizontally off a 56.0-m-high...Ch. 4 - A projectile is launched up and to the right over...Ch. 4 - Sienna tosses a ball from the window of her...Ch. 4 - Some cats can be trained to jump from one location...Ch. 4 - Dock diving is a great form of athletic...Ch. 4 - A graduate student discovers that the only...Ch. 4 - The bola is a traditional weapon used for tripping...Ch. 4 - In three different driving tests, a car moves with...Ch. 4 - A child swings a tennis ball attached to a 0.750-m...Ch. 4 - A Two particles A and B move at a constant speed...Ch. 4 - Prob. 39PQCh. 4 - Prob. 40PQCh. 4 - Prob. 41PQCh. 4 - A pendulum constructed with a bowling ball at the...Ch. 4 - Prob. 43PQCh. 4 - Prob. 44PQCh. 4 - Pete and Sue, two reckless teenage drivers, are...Ch. 4 - Prob. 46PQCh. 4 - Prob. 47PQCh. 4 - A brother and sister, Alan and Beth, have just...Ch. 4 - A man paddles a canoe in a long, straight section...Ch. 4 - Prob. 50PQCh. 4 - Prob. 51PQCh. 4 - Prob. 52PQCh. 4 - Suppose at one point along the Nile River a...Ch. 4 - Prob. 54PQCh. 4 - Prob. 55PQCh. 4 - Prob. 56PQCh. 4 - Prob. 57PQCh. 4 - Two bicyclists in a sprint race begin from rest...Ch. 4 - A particle has a nonzero acceleration and a...Ch. 4 - A golfer hits his approach shot at an angle of...Ch. 4 - You are watching a friend practice archery when he...Ch. 4 - Prob. 62PQCh. 4 - Prob. 63PQCh. 4 - David Beckham has lined up for one of his famous...Ch. 4 - Prob. 65PQCh. 4 - Prob. 66PQCh. 4 - Prob. 67PQCh. 4 - Frequently, a weapon must be fired at a target...Ch. 4 - Prob. 69PQCh. 4 - Prob. 70PQCh. 4 - Prob. 71PQCh. 4 - An observer sitting on a park bench watches a...Ch. 4 - Prob. 73PQCh. 4 - Prob. 74PQCh. 4 - Prob. 75PQCh. 4 - Prob. 76PQCh. 4 - Prob. 77PQCh. 4 - Prob. 78PQCh. 4 - A circus cat has been trained to leap off a...Ch. 4 - Prob. 80PQCh. 4 - An experimentalist in a laboratory finds that a...Ch. 4 - Prob. 82PQ
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Position/Velocity/Acceleration Part 1: Definitions; Author: Professor Dave explains;https://www.youtube.com/watch?v=4dCrkp8qgLU;License: Standard YouTube License, CC-BY