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Read the problems carefully and provide complete solutions with derivation of formulas(integrals and derivatives). Use two decimal places for final answers only. Final answers shown below are incomplete.
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- 2.) A meteor is about to hit a planet and its velocity is defined by v = 5t4 – 5t", where t is in seconds. Find the displacement and acceleration after 5 seconds.1- The "divergence grad 6" can be written as: a: V(V.) b: Vx(V) e: V.(V.) d: V.(V) 2-The acceleration vector in plane polar coordinates is a = (-ro?)e, +(rö + 2ró)eo If a particle moves on a circle path with constant radius b then the radial and transverse components respectively are: a: be and bö b: b and 2bė e: B - bộ and zero d: zero and b- bo? 3- The concept of impulse can be obtained if the force is: a: F(x) b: F(t) e: F(v) d: constant 4- The position vector of a particle can be written in cylindrical coordinates (R, . z) as: a: r=ReR b: r-R eg +o e, + Ze, e: r=R eg +Ze, d: r=ReR + e,-10 10 40 a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k, ii. B = 1+ 2) - k, C = 31 - 1 + 2k . b. The angular velocity of a rotating rigid body about an axis of rotation is given by ai = 4i +j - 2k. Find the linear velocity of a point P on the body whose position vector relative to a point on the axis of rotation is 2i-3j+k. ii. Find the moment of inertia tensor from the given picture. 300 mm P.T.O. iv. Given point P = (1, -2, 3) and vector A = yz i+x1- yx k , express this vector in cylindrical coordinate system. V. a. Show that the contraction of the outer product of the tensors AP and B, is an invariant. b. Show that every tensor can be expressed as the sum of two tensors, one of which is symmetric and the other skew-symmetric in a pair of covariant or contra variant indices. vi. The 4-oz top with radius of gyration about its spin axis of 0.62 in. is spinning at the rate p = 3600 rev/min in the sense shown, with its spin axis making an angle…
- bläi 5 If s is the position at time t of an object moving on a straight line, find the :velocity v and the acceleration a s = (3t – 2)². v=18t-6, a=6 O v=16t-6, a=16 O v=18t-12, a=18 O non of the above1. The instantaneous angular velocity of the crank Q2A i - 3,600° counterclockwise. Q2A = 1.5 in. Find the second instantaneous linear velocity. And draw a graphical interpretation showing the proper length and direction of the velocity arrow of Q2A. Velocity scale: 0.5 in = 10 in/s. Drawing scale: 1:1 2.50 1.50 60° - 60°The figure shows air track setup to verify Newton's law. The distance between the two gates is X = 60 cm. The flag length L=1.5 cm. The kinematic acceleration (ak) is: * 25ms 15ms gate 1 gate 2 puley L=1.5cm X=60cm ******** Gider bangng mass O 6.17 0.5333 5 O 4.71 O 2.9178
- The position of a particle moving along the x-axis is described by x= t^3-108t in where t is the time in seconds. For the time interval t=0 to t=10s. (a) plot the position, velocity, and acceleration as functions of time; (b) find the displacement of the particle: and (c) determine the distance traveled by the particle.The position of an object moving along an x axis is given by x = 3t – 412 + , where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity for the time interval from t 2 s to t = 4 s? (g) Graph x versus t for 02.) A rocket is travelling in another planet where its velocity is defined by v = 4t³ – 6t , where t is in seconds. Find the displacement and acceleration after 5 seconds. tog9ad at 20 A5 deareee WhatThe figure below (not to scale) shows an acceleration-time graph of a body. a (m/s^2) 0 7 t(s) B 27 If the initial velocity was zero, a(0) = a0 = 10.7 m/s^2, a(7) = a7 = -2.2 m/s^2 and the particle's acceleration returns to zero at t = 10s, what will the body's velocity be at t = 10 s? Express your answer to three significant figures in units of m/s (but do not write the units with your answer).ves upward for positive velocity d. Example: Give the positions s= 7(t) of a body moving on a line, with s in meters and t In sccond. Find the body's displacement and average velocity for the given time interval. Also, find the body's speed and acceleration at the endpoints of the interval. During the given interval, wihen does the body change direction 3. s (t/4)- t+t, 0A particle starts from rest at x = -2.5 m and moves along the x-axis with the velocity history shown. Plot the corresponding acceleration and the displacement histories for the 3.2 seconds. Find the time t when the particle crosses the origin. After you have the plots, answer the questions. 3.8 3.2 0.8 1.6 2.4 1.2 Questions Att-0.53 183 m, 2.52 /s, 4,75 m/s? S. At t-0.99 0.258 m/s, m/s X- m. V= 3.8 5. At t=2.83 m. v= m/s, a- m/s2 S. The particle will cross the origin when t Assistance UsedSEE MORE QUESTIONSRecommended textbooks for youElements 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 EducationControl 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:WILEYElements 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 EducationControl 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