Concept explainers
A particle moves along a straight line such that its acceleration is a = ( 4t2 – 2) m/s2 , where t is in seconds. When t = 0, the particle is located 2 m to the left of the origin, and when t = 2 s, it is 20 m to the left of the origin. Determine the position of the particle when t = 4 s.
Learn your wayIncludes step-by-step video
Chapter 12 Solutions
EP ENGR.MECH.:DYNAMICS-STANDALONE ACC.
Additional Engineering Textbook Solutions
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Engineering Mechanics: Statics
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
- 1. The velocity of a particle is given by v = {16t²i + 4t³j+ (5t + 2)k} m/s, 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=2s. Also, what is the x, y, z coordinate position of the particle at this instant?arrow_forwardA body moves along a linear path and its rate of change of velocity varies with time and is written as a=2-3t, where t is the time in second. After 5 second, from start of observation its velocity is determined to be 20 m/s. After 10 second from start of observation, the body is at 85 m far from the origin. Determine the following:a. Rate of change of velocity and velocity at the start of motion.b. Distance from the origin at the start of observationc. Time after start of observation in which the velocity becomes zero.arrow_forwardThe rectangular coordinates of a particle which moves with curvilinear motion are given by x = 9.75t + 1.25t²-0.60t3 and y=6.12 + 10.89t-2.01t², where x and y are in millimeters and the time t is in seconds, beginning from t= 0 Determine the velocity v and acceleration of the particle when t-7s. Also, determine the first time that the welocity of the particle makes an angle of 27" with the positive-anis V= 13 25 i i [ mmsarrow_forward
- When a particle is constrained to move in a straight line, its position coordinates are given by s=2t3 - 24t + 6, where s is measured in meters from a convenient origin and t is in seconds. Determine the acceleration of the particle when v=30 m/s (Rectelinear Kinematics)arrow_forwardThe velocity of a particle which moves along the s axis is given by v = 7 - 4t + 7t3/2, where t is in seconds and v is in meters per second. Evaluate the position s, velocity v, and acceleration a when t = 4 s. The particle is at the position so = 4 m when t = 0. Answers: S= V = a = i i i m m/s m/s²arrow_forward3. The motion of the particle along a straight line is governed by the relation a = t³ – 2t2 + 7 where a is the acceleration in m/s? andt is the time in seconds. At time t velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at time t = 2 seconds. * A second, the 0.5 А second V = ..m/s d 25 marrow_forward
- The position of a particle is defined by x=2t3-18t2+48t-16, where x in m and t in s. Determined 1) when the velocity is zero, 2) the velocity, the acceleration and * .the total distance traveled at t=2sarrow_forwardThe velocity of a car traveling along a straight line is given by v = (4 · t² – 7 · t) · ft where t is in S seconds. Initially, s 2 ft when t = 0. %3D a. Determine the position s of the car when t = 7 s. b. Determine the total distance travelled during the time interval t = 0 s to t = 7 s. c. Determine the acceleration a at t = 2 s .arrow_forward60 ft/s Q1: Car A starts from rest at straight road with a constant acceleration of 4 ft/s? until it reaches a speed of 70 ft/s. Afterwards it maintains this speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 60 ft/s. Determine the distance traveled by car A when they pass t = 0 and travels along a 6000 ft each other.arrow_forward
- The acceleration of a particle is defined as a = 9 – 3t2. The particle starts at t 0 with v = 0 and x = 5 m. Determine: 1. The time when the velocity is again zero. 2. The position and velocity when t = 4 s Select one: A. t = 3; x(4) = 13 m and v(4) = -28 m/s %3D B. t = 1; x(4) = 13 m and v(4) = -28 m/s %3D !i! C. t = 0; x(4) = 13 m and v(4) = -28 m/s %3D %3D D. t = 3; x(4) = 13 m and v(4) = 28 m/s %3Darrow_forwardText:The particle travels along the path defined by the parabola y=0.5x². If the component of velocity along the x-axis is v=5t m/s, where "t" is in seconds, determine the particle's distance from the origin and the magnitude of its acceleration when t=1s. When t=0, x,=0, yo=0. y=0.5xarrow_forward1. A particle moves along a straight line such that its acceleration is a = (42 - 2) m/s?where t is in seconds. When t = 0, the particle is located 2m to the left of the origin,and t = 2s, it is 20m to the left of the origin. Determine the position of the particlewhen t = 4 s. 2. A particle is moving along a straight line with the acceleration a =12t - 3t2 ft/52,where t is in seconds. Determine the velocity and the position of the particle as afunction of time. When t = 0, v = 0 and s = 15 ft. 3. A ball is released from the bottom of an elevator which is travelling upward with avelocity of 6 m/s. The ball strikes the bottom of the elevator shaft in elevator shaft in3s. Determine the height of the elevator from the bottom of the shaft to the instantthe ball is released, and find the velocity of the ball when it strike the bottom of theshaft. 4. A particle moving along a straight line is subjected to a deceleration a =-20m/52where v is in m/s. If it has a velocity v = 8 m/s s = 10 m when…arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY