Concept explainers
The vector position of a particle varies in time according to the expression
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Bundle: Physics For Scientists And Engineers With Modern Physics, Loose-leaf Version, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Single-term
- The acceleration of a particle is a constant. At t = 0 the velocity of the particle is (10i ^ + 20j ^ )m/s. At t = 4 s the velocity is 10j ^ m/s. (a) What is the particle’s acceleration? (b) How do the position and velocity vary with time? Assume the particle is initially at the origin.arrow_forwardv → = ( 6 t − 4 t 2 ) i ^ − 8 j ^. Here v → is in meters per second and t in seconds. (a) What are the position, speed, and acceleration of the particle when t = 4.3 s? (b) When (if ever) is the acceleration zero? Prove your answer. (c) When (if ever) is the velocity zero? Prove your answer.arrow_forwardA particle is moving in three dimensions and its position vector is given by; r(t) = (4t² + 1.7t) î + (1.5t − 2.1)ĵ + (2.7t³ + 2t) k where r is in meters and t is in seconds. Determine the magnitude of the instantaneous velocity at t = 3s. Express your answer in units of m/s using one decimal place. Answer:arrow_forward
- Problem 2: The position of a particle is given by the following expression, where t is time measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k. Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s? Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s? Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t = 1.65 s? Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65 s? Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s make with the z axis?arrow_forwardAn object has an acceleration as a function of time given by (in m/s2): a = (7t2 + 2t) i + (5t3 + 8) j Given: at t=0.0 s, the object is at the origin with a velocity of 0.0 m/s. What is the magnitude of its position (in m) when t= 6 s ?arrow_forwardA fish swimming in a horizontal plane has velocity given by v i j i = 4ˆ + ˆ m/s at a point in theocean where the position relative to a certain rock is r i j i = 10ˆ − 4 ˆ m. After the fish swimswith constant acceleration for 20.0 s, its velocity is v i j = 20ˆ − 5 ˆ m/s.a) What are the components of the acceleration of the fish?b) What is the direction of its acceleration with respect to the unit vector along the x axis?c) If the fish maintains constant acceleration, where is it at t = 25.0 s and in what direction isit moving?arrow_forward
- The acceleration of a particle moving along a straight line is a = (11 - 1.0s) m/s², where s is in meters. If v = 0 when s = 0, determine the magnitude of the particle's velocity when s = 7.0 m.arrow_forwardAn ion's position vector is initially 7 = (-3,9 m )i + (-8.6 m )j + (-3.4 m )k, and 9.3 s later it is 7 = (-2.6 m )i + (7.3 m )ĵ + (1.0 m )R. In unit-vector notation, what is its average velocity during the 9.3 s? Number i k Units m/sarrow_forwardThe velocity of a particle (in meters per second) is given by v = 16t²i + 4t³j+ (5t + 2)k, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?arrow_forward
- a particle initially at position r=(2j+3k)m moves to r=(2i+3j-2k)m in 2s. Find the magnitude of the particles average velocity. If the particles acceleration is a=(2i-k) m/s^2 , find the angle between the particles acceleration and displacementarrow_forwardThe 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?.arrow_forwardAn object has an acceleration as a function of time given by (in m/s2): A = (3t2 + 3t) i + (7t3 + 6) j Given: at t=0.0 s, the object is at the origin with a velocity of 0.0 m/s. What is the magnitude of its velocity (in m/s) when t= 4 s ?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning