Q1. A particle starts from rest at and moves along the with the velocity history shown. Plot the corresponding displacement and acceleration histories for the seconds. Given Required 3.0 1.0 0 0.5 L 1 1.0 1 1.5 20
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- The figure shows a plot of potential energy U versus position x of a 0.270 kg particle that can travel only along an x axis under the Influence of a conservative force. The graph has these values: UA9.00 ). Uc 20.0 J and Ug 24.0J. The particle is released at the point where Uforms a "potential hill" of "height" Ua 12.0J. with kinetic energy 7.50 J.What is the speed of the particle at la) -3.50m and (b)x - 6.50 m? What is the position of the turning paint on (c) the right side and (d) the left side?A 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 UsedFind the total distance traveled by a particle given its velocity function Question Find the total distance traveled by a particle according to the velocity function v(t) =-4t + 6 m/sec over the time interval 0, 5|. Enter your answer as an exact fraction if necessary and do not include units in your answer. Provide your answer below: • Previous Nex
- 1. The graph in Fig. A shows the velocity of an ambulance vehicle driver plotted as a function of time. How far does the officer go in the first 3 seconds? The first 7 seconds? The first 11 seconds? Vx (m/s) 50 45 40 35 30 25 Fig. A 20 15 10 5 t (s) 2 4 6 !8 10 12 14 7 11 3.A particle moves along the x-axis with the velocity history shown. If the particle is at the position x = -2 in, at time t = 0, plot the corresponding displacement history for the time interval Osts 8 sec. After you have the plot, answer the questions as a check on work. u, in./sec 3 o Questions: When t= 1.4s, x= Whent = 4.8 s, x= When t = 7.0 s. x= i i i For the time interval Ost≤8 sec. The net dispalcement Ax= The total distance traveled total 6 -6 i i 8 t, sec in. in. in. in. in.03:31 Given-Assign... External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: PND? and a, = b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750 kg/m and the dynamic viscosity is 0.2 N.s/ m² . For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s / m². IN =1 kgm
- (C.t-1) m/s, where Cis a constant and t is the Q8. The acceleration of a particle moving along a straight line is a time in s. If the constant Cis 3.6, and the initial velocity vo = 2.1 m/s at time t = 0, determine the particle's velocity when time t = 2 s. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper Sl unit. Answer: =A snowboarder’s velocity is tracked by a pulse-laser velocimeter as she descends the slope. These velocity data are stored and analyzed via an embedded curve fitting procedure to determine a velocity function of v(t) = 1.5t2 + 2t + 2 (t is time in seconds and v is velocity in ft/s). At time equal 0, position (x) is zero. Find her position (e.g., distance traveled), velocity and acceleration formulations and values of each when time equals 15 seconds. Clearly write the formulas before finding respective values at t = 15 seconds!6. A ball is thrown straight up in the air at time t = 0. Its height y(t) is given by y(t) = vot - 791² (1) Calculate: (a) The time at which the ball hits the ground. First, make an estimate using a scaling analysis (the inputs are g and vo and the output is the time of landing. Think about their units and how you might construct the output using the inputs, just by matching units). Solve the problem exactly. Verify that the scaling analysis gives you (almost) the correct answer. (b) The times at which the ball reaches the height v/(4g). Use the quadratic formula. (c) The times at which the ball reaches the height v/(2g). You should find that both solutions are identical. What does this indicate physically? (d) The times at which the ball reaches the height v/g. What is the physical interpretation of your solutions? (e) Does your scaling analysis provide any insight into the answers for questions (a-e)? Discuss. (Hint: Observe how your answers depend on g and vo).
- The time variation of the position of a particle in rectilinear motion is given by x = 2 + P+ 2t. If v is the velocity and a the acceleration of the particle in consistent units, the motion started with (b) v = 0, a = 2 (d) v = 2, a = 2 (a) v = 0, a = 0 %3D %3D %3D (c) v = 2, a = 0 %3D %3DThe electronic throttle control of a model train is programmed so that the train speed varies with position as shown in the plot. Determine the time t required for the train to complete one lap. [Answer: 50.8s] 1m 1m 2 m 0.250 0.125 2 2+5 2+n 4+n 2+ 4+2n 3n Distance s, m Speed v, m/s1. The wheel starts rotating from rest, 4) if its angular velocity W as a function of angular position 0 is w=0.1-0², where O is in radian, and its radius ris 0.2 m, what is the magnitude of the normal linear acceleration (in m/s2) of point Pafter the wheel has turned 1.1 revolution(s) from rest. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Your Answer: Answer