Example 2:A particle moving along a straight line is subjected to a deceleration a = (-2v) m/s², where v is in m/s. If it has a velocity v = 8 m/s and a position s t = 0, determine its velocity and position when t = 4 s. = 10 m when %3D %3D
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- 1. The position of a particle moving along the x-axis is described by x = t – 108t in where t is the time in sec. For the time interval t= 0 to t = 10 s, (a) plot the position, velocity, and acceleration as a function of time (b) find the displacement of the particle and (c) determine the distance traveled by the particle.The 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).The diagram below represents a swimmer. The swimmer is capable to swim in a still water with a velocity Vị = 1 m's. He aims his body directly across a 100 m wide river whose current has a velocity V;=2 m/s. Use this diagram to answer questions 1 through 3. 1. The time it will take for the swimmer to cross the river is .. (A) 10 sec (B) 20 sec (C) 50 sec (D) 100 sec 2. How far downstream will he land? The correct answer is (A) 100 m (B) 200 m (C) 150 m (D) 180 m
- 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.Dynamics Under rectilinear motion the behavior of velocity is given by v=1+x^2 , where v is in ft/s and x is in ft. When x = 0, t = 0. a. Determine a relation a vs x b. Determine a relation t vs x c. Calculate the acceleration when x = 2 d. Calculate the velocity and acceleration when t = 4.(d) The velocity versus position graph of a motorcycle is given in Figure 1.3 below. Determine its acceleration at s=150 ft (4 Marks) v (ft/s) 50 10 200 400 2 -s (ft)
- 4. 2) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions 4 1.0 ft, and 2 = 1.7 ft, VA = 4.9 ft/s, aa = 2.6 ft/s2, and the angle 0 = 27°, determine the speed of point B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. В 12 D a Your Answer: Answer units 1,As shown in the figure. A plot of potential energy U versus position x of a 2 kg particle that can move along x-axis. The graph has these values U_A=9J, U_C=20J and U_D=24J. The particle is released at position x=5 m with kinetic energy 4 J where the potential energy is U_B=12 j. What is the kinetic energy of the particle at x =3.5 m. Upt ... Uc UAF-- 4 6 7 x (m) A) 8J B none of them C 7J D 7.5JTOPIC: Equation of Motion (NORMAL AND TANGENTIAL) Fn= Man Ft= Mat Given a 1400 kg car that travels along a road with increasing vertical profile y = 0.0003x². If the constant velocity of the car is 30 m/s. of the distance is at 210m, Determine the x-component of the velocity (m/s) of the car. Compute the total force (KN). PLEASE ANSWER WITH A COMPLETE AND DETAILED SOLUTIONS. THANK YOU
- 1. A box slides down a ramp with position vector given by r= 0.5t i + 3f² j + 8t k (m), where t is in s. At t = 3 s, what is the box's velocity and acceleration? What is the box's speed?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.SHOW THE SOLUTION: One morning, Connie walks from her house to go to a store that is 500 ft, S 40o W from her house. She starts walking 120 ft, SW; then continues walking 100 ft, 10o S of E; then sees a friend who is 700 ft, 30o N of E from where she is. What is her friend’s location, (magnitude and direction) relative to her house? (Answer: 667.54 ft, 21.79o N of E) From her friend’s location, how far and in what direction should Connie walk to finally get to the store? (Answer: 1133.08 ft, 33.83o S of W)