The x-coordinate of a particle in curvilinear motion is given by x = 3.9t° - 1.6t where x is in feet and tis in seconds. The y-component of acceleration in feet per second squared is given by ay = 5.2t. If the particle has y- components y = 0 and vy = 3.7 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 2.8 sec. Sketch the path for the first 2.8 seconds of motion, and show the velocity and acceleration vectors for %3D t= 2.8 sec. Answers: V = i ft/sec i ft/sec?
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- The velocity of a particle (in meters per second) is given by v = 16t'i+ 4tj + (5t + 2)k, wheret is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant? a = 75.16 m s^-2 ;r = (36.67, 10, 8) a = 80.16 m s^-2;r = (42.67, 16, 14) a = 85.16 m s^-2;r = (48.67, 24, 20) O None of the choicesA particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.The x-coordinate of a particle in curvilinear motion is given by x = 2.0t³ - 3.0t where x is in feet and t is in seconds. The y-component of acceleration in feet per second squared is given by ay = 4.0t. If the particle has y-components y = 0 and vy = 4.0 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 2.0 sec. Sketch the path for the first 2.0 seconds of motion, and show the velocity and acceleration vectors for t = 2.0 sec. Answers: V = a = i i ft/sec ft/sec²
- The displacement of a particle is given by s = 2t³ - 42t² + 120t - 68 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 16 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 3.3 sec, S= i ft, v = i ft/sec, a = i ft/sec At t = 8.9 sec, S = ft, v = i ft/sec, a = i ft/sec Att = 14.2 sec, S= i ft, v = i ft/sec, a = i ft/sec The velocity is zero when t = i i sec and when t = i secA particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 4.9t2 - 7.0t and y = 6.1t2 - t/5.1. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 2.4 s. Answers: When t - 2.4 s, i mm/s, e, = i i mm/s?, ex- i a =You are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the +y direction is downward and neglecting air resistance, the vertical displacement of an object released from rest is given by y − y0 = 1/2gplanett2, where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of y − y0 in meters and plot your data with t2 on the vertical axis and y − y0 on the horizontal axis. Your data is fit closely by a straight line that has slope 0.300 s2/m. Based on your data, what is the value of gplanet?
- Ana runs southeast at constant velocity, with velocity components Vx = 5.6 m/s, Vy= −1.4 m/s. What is the magnitude of Ana’s velocity?The velocity of the wind relative to the water is crucial to sailboats. Suppose a sailboat is in an ocean current that has a velocity of 2.1 m/s in a direction 27° east of north relative to the Earth. It encounters a wind that has a velocity of 4.4 m/s in a direction of 49° south of west relative to the Earth. 1. What is the magnitude of the velocity of the wind relative to the water, in meters per second? 2. What is the angle of the velocity of the wind relative to the water degrees south of west?A golf ball is driven with the initial conditions shown in the figure. If the wind imparts a constant horizontal deceleration of 3.9 ft/sec2, determine the values of r, r˙, r¨, θ, θ˙, and θ¨ when t = 1.18 sec. Take the r-coordinate to be measured from the origin.
- 2/63 The x-coordinate of a particle in curvilinear motion is given by x = 2t³ - 3t, where x is in feet and t is in seconds. The y-component of acceleration in feet per second squared is given by a, = 4t. If the particle has y-components y = 0 and y = 4 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 2 sec. Sketch the path for the first 2 seconds of motion, and show the velocity and accel- eration vectors for t = 2 sec.A particle is moving along a curved path. At a certain instant when the slope is 0.75, ax = 2 m/s2 and ay = 3 m/s2. Find the value of an. the final answer must be 3 decimal places.A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 1.9t²-3.1t and y-6.1t2-t3/1.2. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t - 4.3 s. Answers: When t = 4.3 s, V= a- i mm/s, ex- mm/s², 0,- i