Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 3, Problem 43AP
(a)
To determine
The differentiation of position vector
(b)
To determine
The physical quantity about an object that is represents by
Introduction: The rate of change of position of an object with time is known as velocity of that object.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A particle moves in the xy plane, starting from the origin at t = 0 with an initial velocity having an x component of 20 m/s and a y component of 215 m/s. The particle experiences an acceleration in the x direction, given by ax =4.0 m/s2.(A) Determine the total velocity vector at any later time. (B) Calculate the velocity and speed of the particle at t = 5.0 s and the angle the velocity vector makes with the x axis. (C) Determine the x and y coordinates of the particle at any time t and its position vector at this time.
A lift is coming from 8th floor and is just about to reach 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?
(a) x < 0, v < 0, a > 0
(b) x > 0, v < 0, a < 0
(c) x > 0, v < 0, a > 0
(d) x > 0, v > 0, a < 0
The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?
Chapter 3 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 3.2 - Which of the following are vector quantities and...Ch. 3.3 - Prob. 3.2QQCh. 3.3 - If vector B is added to vector A, which two of the...Ch. 3.4 - Choose the correct response to make the sentence...Ch. 3.4 - Prob. 3.5QQCh. 3 - Two points in the xy plane have Cartesian...Ch. 3 - Prob. 2PCh. 3 - The polar coordinates of a certain point are (r =...Ch. 3 - Prob. 4PCh. 3 - Why is the following situation impossible? A...
Ch. 3 - Prob. 6PCh. 3 - A force F1 of magnitude 6.00 units acts on an...Ch. 3 - Three displacements are A=200m due south, B=250m...Ch. 3 - The displacement vectors A and B shown in Figure...Ch. 3 - A roller-coaster car moves 200 ft horizontally and...Ch. 3 - Prob. 11PCh. 3 - A person walks 25.0 north of east for 3.10 km. How...Ch. 3 - Your dog is running around the grass in your back...Ch. 3 - Given the vectors A=2.00i+6.00j and B=3.00i2.00j,...Ch. 3 - The helicopter view in Fig. P3.15 shows two people...Ch. 3 - A snow-covered ski slope makes an angle of 35.0...Ch. 3 - Prob. 17PCh. 3 - Vector A has x and y components of 8.70 cm and...Ch. 3 - The vector A has x, y, and z components of 8.00,...Ch. 3 - Given the displacement vectors A=(3i4j+4k)m and...Ch. 3 - Vector A has a negative x component 3.00 units in...Ch. 3 - Three displacement vectors of a croquet ball are...Ch. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Use the component method to add the vectors A and...Ch. 3 - Prob. 26PCh. 3 - A man pushing a mop across a floor causes it to...Ch. 3 - Figure P3.28 illustrates typical proportions of...Ch. 3 - Prob. 29PCh. 3 - In an assembly operation illustrated in Figure...Ch. 3 - Review. You are standing on the ground at the...Ch. 3 - Why is the following situation impossible? A...Ch. 3 - Prob. 33PCh. 3 - Prob. 34APCh. 3 - A person going for a walk follows the path shown...Ch. 3 - A ferry transports tourists between three islands....Ch. 3 - Two vectors A and B have precisely equal...Ch. 3 - Two vectors A and B have precisely equal...Ch. 3 - Review. The biggest stuffed animal in the world is...Ch. 3 - Prob. 40APCh. 3 - Prob. 41APCh. 3 - Prob. 42APCh. 3 - Prob. 43APCh. 3 - Vectors A and B have equal magnitudes of 5.00. The...Ch. 3 - A rectangular parallelepiped has dimensions a, b,...Ch. 3 - A pirate has buried his treasure on an island with...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Vectors A= 1.00i -2.00j and B=3.00i +4.00j what are the magnitude and direction of vector C=A+B ? what is the length of the path the object followed during the time interval from t=0.0s and t=9.0s?arrow_forwardA spacecraft is traveling with a velocity of v0x = 5505 m/s along the +x direction. Two engines are turned on for a time of 846 s. One engine gives the spacecraft an acceleration in the +x direction of ax = 1.00 m/s2, while the other gives it an acceleration in the +y direction of ay = 8.65 m/s2. At the end of the firing, find vx and vy. a) vx = _________m/s (b) vy = _________m/sarrow_forwardYou encounter a moving walkway that is 81 m long and has a speed of 2.1 m/s relative to the ground. How long would it take you to cover the 81 m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.6 m/s relative to the walkway? Express your answer using one significant figure.arrow_forward
- A spacecraft is traveling with a velocity of Vox=5950 m/s along the +x direction. Two engines are turned on for a time of 817 s. One engine give the spacecraft an acceleration in the +x direction of ax=1.18 m/s2, while the other gives it an acceleration in the +y direction of ay=7.30 m/s2. At the end of the firing, what is (a) Vx and (b) Vy?arrow_forward. What is the magnitude and direction of the PQ→ with tail and head points P(-6, 0) and Q(2, 4)? a 8.9 units, 26.6° north of east b 8.9 units, 63.4° north of east c 13.4 units, 180° west d 13.4 units, 0° eastarrow_forwardAt t = 0 the coordinates of a particle are x = 0, y = 1.98 m. At a time 0.95 s later, its coordinates are x = 3.21 m, y = 4.20 m. Find the components of the particle's average velocity during this time interval. vx = vy =arrow_forward
- A fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axisarrow_forwardA fish swimming in a horizontal plane has velocity i = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is i = (16.0 î − 3.20 ĵ) m. After the fish swims with constant acceleration for 15.0 s, its velocity is = (21.0 î − 6.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis(c) If the fish maintains constant acceleration, where is it at t = 30.0 s? x = 542.5 Remember that you can treat the motions in the x and y directions separately. Each is then treated exactly as you would the one-dimensional case. m y = m In what direction is it moving? ° counterclockwise from the +x-axiarrow_forwardAn object has position given by the vector r = [3.0m + (6.0m/s)t] i + [2.0m - (2.0m/s2)t2] j, where quantities are in SI units. What is the speed of the object at t = 3.0s?arrow_forward
- A football is placed at rest on the field with initial coordinates x0 = 0 and y0 = 0. The ball is then kicked and thereby given an initial velocity of magnitude v0 = 23.6 m/s and direction θ0 = 36.3o above the horizontal. Ignore the effects of air resistance. Initial horizontal component of the velocity v0x = Initial vertical component of the velocity v0y = Horizontal component of the acceleration ax = Vertical component of the acceleration ay = Enter the equation for the horizontal position versus time, x(t) = Enter the equation for the vertical position versus time, y(t) = Enter the equation for the horizontal velocity versus time, vx(t) = Enter the equation for the vertical velocity versus time, vy(t) = Enter the equation for the total velocity versus time, v(t) = Enter the equation for the angle of the velocity vector versus time, θ(t)= Enter the maximum height of the football Enter the range of the football Enter the time it takes for the football to reach its maximum…arrow_forwardThe coordinates of a particle moving in the XY plane are given as function of time by: X = 5m + ( 7 m/s^4) t ^4 Y = ( 10 m/s)t + (3 m/s^5)t ^5 Find the position vector of the body at t = 3.5 seconds and instantaneous acceleration of the body at t = 3.5 secarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY