Concept explainers
To Find: Magnitude of the displacement is less than or more than the distance travelled.
Answer to Problem 1P
Magnitude of the displacement is always less than or equals to the distance travelled.
Explanation of Solution
Introduction:
Distance can be defined as the total path length travelled by a body. Its S.I. unit is
Where,
Displacement can be defined as the path difference between the initial and final position of the body. It is the minimum distance between two points.
Its S.I. unit is
Here are some examples,
Consider a body is travelling along a straight line from A to B and then B to C.
Total distance travelled by the body
Displacement of the body
Consider a body is moving in a circular path of radius
Since,
Therefore, distance travelled > displacement
Total distance traveled by the body = circumference of the circle
Displacement of the body = final position − initial position.
Here body come to its initial position after revolution
Therefore,
final position = initial position
hence,
Displacement of the body
Again, distance > displacement
Consider a body travelling in a straight line from A to B
Distance travelled = AB
Displacement = AB
Here, Displacement = Distance travelled
Conclusion:
Displacement of a body can never be greater than the distance travelled by the body. It is either equal to the distance travelled by the body or less than it.
Want to see more full solutions like this?
Chapter 3 Solutions
Physics for Scientists and Engineers
- If you know the position vectors of a particle at two points along its path and also know the time it took to get from one point to the other, can you determine the particle’s instantaneous velocity? Its average velocity? Explain.arrow_forwardIf the velocity of a particle is zero, can the particle's acceleration be zero? Give an example. If the velocity of a particle is not zero, can the particle's acceleration be zero? Give an example.arrow_forward2) The position of a particle traveling along a curved path is s = (3t3 - 4t² + 4) m, where t is in seconds. When t = 2 s, the particle is at a position on the path where the radius of curvature is 25 m. Determine the magnitude of the particle's acceleration at this instant.arrow_forward
- 4) Find the time or times in the given time interval when velocity and acceleration vectors are orthogonal; r(t) = i + (5 cos t)j + (3 sin t)k, 0arrow_forwardA cross-country skier skis 1.0 km north and then 2.0 km east. How far and in what direction is she from the starting point? What are the magnitude and direction of her resultant displacement? (Complete solution)arrow_forwardWhich of the following objects is undergoing uniform circular motion> a. An object speeding up at a constant rate while following a circular path. b. An object whose velocity is changing at a constant rate in a given direction. c. An object undergoing acceleration with a constant magnitude directed towards the centre of its circular path. d. An object that is traveling at constant speed around a circular path.arrow_forwardQuestion (äbäi 4) If vector B is added to vector Á, the result is 6i + j. If B is subtracted from ä, the result is -4i+ 7i. What is the magnitude of A 1.2 2.3 4.1 6.2 7.1arrow_forwardRaindrops hitting the side windows of a car in motion often leave diagonal streaks even if there is no wind. Why? Is the explanation the same or different for diagonal streaks on windshield? Explain in 10 sentencesarrow_forward7) A particle moves along a plane circular path of radius r equal to 1 ft. The position OA is given as a function of time as 0 = 6 sin(5t) rad, where t is in seconds. What are the rectangular compo- nents of velocity and acceleration for the particle at t = = sec? 8arrow_forwardUnder what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?arrow_forwardIf two vectors are equal, what can you say about their components? What can you say about their magnitudes? What can you say about their directions?arrow_forwardA pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m). (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P3.46. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure P3.46arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegePhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning