Essential University Physics: Volume 1 (3rd Edition)
3rd Edition
ISBN: 9780321993724
Author: Richard Wolfson
Publisher: PEARSON
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Textbook Question
Chapter 3, Problem 49P
A particle’s position is
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A particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j,
undergoes an acceleration ở = 2t²î + 4ĵ in SI units.
For t = 10 s;
a) Calculate the velcoity v= vxI+ vy®.
b) Calculate the position r= x+ y.
c) What are the magnitudes of the velocity and the position vector of
the particle?
d) Find also the angle each vector is making with the x-axis at that
time.
The position vector of a particle is given as
r = (t^2-6t+8)i + (t^2-9)j
Find the magnitude and direction of the particle’s position, velocity, and acceleration at ? = 2?. Find the magnitude and direction of the particle’s displacement, average velocity and average acceleration for the time period ? = 2? to ? = 3?.
The position vector of a particle moving in the xy-plane is given by
(At, Bt¹)
r =
where t is the time in seconds. A and B are constants with the values
A 4.5 ms 1, B = 8.0 ms-4.
=
ms¹,
(a) Calculate the magnitude of the particle's displacement from the
origin at time t = 2.0s.
(b) Find the particle's acceleration vector, a, at time t = 2.0s.
Chapter 3 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Ch. 3.1 - Which vector describes a displacement of 10 units...Ch. 3.2 - An object is accelerating downward. Which, if any,...Ch. 3.3 - An airplane is making a 500-km trip directly north...Ch. 3.4 - An object is moving initially in the +x-direction....Ch. 3.5 - Two projectiles are launched simultaneously from...Ch. 3.6 - An object moves in a horizontal plane with...Ch. 3 - Under what conditions is the magnitude of the...Ch. 3 - Can two vectors of equal magnitude sum to zero?...Ch. 3 - Repeat Question 2 for three vectors. 2. Can two...Ch. 3 - Can an object have a southward acceleration while...
Ch. 3 - Youre a passenger in a car rounding a curve. The...Ch. 3 - In what sense is Equation 3.8 really two (or...Ch. 3 - Is a projectiles speed constant throughout its...Ch. 3 - Is there any point on a projectiles trajectory...Ch. 3 - How is it possible for an object to be moving in...Ch. 3 - Youre in a bus moving with constant velocity on a...Ch. 3 - Which of the following are legitimate mathematical...Ch. 3 - You would probably reject as unscientific any...Ch. 3 - You walk west 220 m, then north 150 m. What are...Ch. 3 - An ion in a mass spectrometer follows a...Ch. 3 - A migrating whale follows the west coast of Mexico...Ch. 3 - Vector A has magnitude 3.0 m and points to the...Ch. 3 - Use unit vectors to express a displacement of 120...Ch. 3 - Find the magnitude of the vector 34 + 13 m and...Ch. 3 - (a) Whats the magnitude of + ? (b) What angle...Ch. 3 - Youre leading an international effort to save...Ch. 3 - An object is moving at 18 m/s at 220...Ch. 3 - A car drives north at 40 mi/h for 10 min, then...Ch. 3 - An objects velocity is v = ct3 + d, where t is...Ch. 3 - A car, initially going eastward, rounds a 90 curve...Ch. 3 - What are (a) the average velocity and (b) the...Ch. 3 - An ice skater is gliding along at 2.4 m/s, when...Ch. 3 - An object is moving in the x-direction at 1.3 m/s...Ch. 3 - Youre a pilot beginning a 1500-km flight. Your...Ch. 3 - You wish to row straight across a 63-m-wide river....Ch. 3 - A plane with airspeed 370 km/h flies...Ch. 3 - A flock of geese is attempting to migrate due...Ch. 3 - The position of an object as a function of time is...Ch. 3 - Youre sailboarding at 6.5 m/s when a wind gust...Ch. 3 - You toss an apple horizontally at 8.7 m/s from a...Ch. 3 - A carpenter tosses a shingle horizontally off an...Ch. 3 - An arrow fired horizontally at 41 m/s travels 23 m...Ch. 3 - Droplets in an ink-jet printer are ejected...Ch. 3 - Protons drop 1.2 m over the 1.7-km length of a...Ch. 3 - If you can hit a golf ball 180 m on Earth, how far...Ch. 3 - Chinas high-speed rail network calls for a minimum...Ch. 3 - The minute hand of a clock is 7.50 cm long. Find...Ch. 3 - How fast would a car have to round a 75-m-radius...Ch. 3 - Estimate the acceleration of the Moon, which...Ch. 3 - Global Positioning System (GPS) satellites circle...Ch. 3 - Two vectors A and B have the same magnitude A and...Ch. 3 - Prob. 46PCh. 3 - Let A = 15 40 and B = 31 + 18k. Find C such that...Ch. 3 - A biologist looking through a microscope sees a...Ch. 3 - A particles position is r = (ct2 2dt3) + (2ct2 ...Ch. 3 - For the particle in Problem 49, is there any time...Ch. 3 - Youre designing a cloverleaf highway interchange....Ch. 3 - An object undergoes acceleration 2.3 + 3.6 m/s2...Ch. 3 - The New York Wheel is the worlds largest Ferris...Ch. 3 - A ferryboat sails between towns directly opposite...Ch. 3 - The sum of two vectors, A + B, is perpendicular to...Ch. 3 - Write an expression for a unit vector at 45...Ch. 3 - An object is initially moving in the .x-direction...Ch. 3 - A particle leaves the origin with its initial...Ch. 3 - A kid fires a squirt gun horizontally from 1.6 m...Ch. 3 - A projectile has horizontal range R on level...Ch. 3 - You throw a baseball at a 45 angle to the...Ch. 3 - In a chase scene, a movie stuntman runs...Ch. 3 - Standing on the ground 3.0 m from a building, you...Ch. 3 - Derive a general formula for the horizontal...Ch. 3 - Consider two projectiles launched on level ground...Ch. 3 - You toss a protein bar to your hiking companion...Ch. 3 - The table below lists position versus time for an...Ch. 3 - A projectile launched at angle to the horizontal...Ch. 3 - As an expert witness, youre testifying in a case...Ch. 3 - Show that, for a given initial speed, the...Ch. 3 - A basketball player is 15 ft horizontally front...Ch. 3 - Two projectiles are launched simultaneously from...Ch. 3 - Consider the two projectiles in GOT IT? 3.5....Ch. 3 - The portion of a projectiles parabolic trajectory...Ch. 3 - A jet is diving vertically downward at 1200 km/h....Ch. 3 - Your alpine rescue team is using a slingshot to...Ch. 3 - If you can throw a stone straight up to height h....Ch. 3 - In a conversion from military to peacetime use, a...Ch. 3 - A soccer player can kick the ball 28 m on level...Ch. 3 - A diver leaves a 3-m board on a trajectory that...Ch. 3 - Prob. 81PCh. 3 - You're a consulting engineer specializing in...Ch. 3 - Differentiate the trajectory Equation 3.14 to find...Ch. 3 - Your medieval history class is constructing a...Ch. 3 - Generalize Problem 84 to find an expression for...Ch. 3 - (a) Show that the position of a particle on a...Ch. 3 - In dealing with nonuniform circular motion, as...Ch. 3 - Repeat Problem 87, now generalizing to the case...Ch. 3 - Alice (A), Bob (B), and Carrie (C) all start from...Ch. 3 - Alice (A), Bob (B), and Carrie (C) all start from...Ch. 3 - Alice (A), Bob (B), and Carrie (C) all start from...Ch. 3 - Alice (A), Bob (B), and Carrie (C) all start from...
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