The position of a particle moving in the xy –plane is given by ř(t) = (3t² – t³)î + (t*)ĵ + (– 6t)k. What is the average acceleration of the particle over the time interval between t = 1 s and t = 2 s? %3D
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- The velocity of a particle is given by v = 23t2 - 110t + 52, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6.4 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.8 s, V = i m/s, a = i m/s2 When t = 3.7 s, V = i m/s, a = i m/s? When t = 4.7 s, V = i m/s, a = i m/s? When a = 0, V = m/sA particle’s velocity along the x-axis is described by v(x) = A x + B x2, where x is in meters, v is in meters per second, A = 3.56, and B = -1.5 what is the acceleration, in meters per second squared, of the particle position at x = 2.31m?The displacement of a particle is given by s = 3t3 - 53t2 + 115t - 62 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions.Questions: At t = 3 sec, s = ft, v = ft/sec, a = ft/sec2 At t = 7.7 sec, s = ft, v = ft/sec, a = ft/sec2 At t = 11.5 sec, s = ft, v = ft/sec, a = ft/sec2 The velocity is zero when t = sec and when t = sec
- A particle moving along the x-axis has velocity function v(t) = t³ sin t. How far does the particle travel from time t = 0to t = π?7(t) = t? i+ In(t)² j+ sin nt k where t is The position of a particle is given by measured in seconds and is measured in meters. Find the velocity, acceleration, and speed functions. What are the position, velocity, speed, and acceleration of the particle of at t = 3 seconds ?Problem 2: The position of a particle is given by the following expression, where t is time measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k. Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s? Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s? Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t = 1.65 s? Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65 s? Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s make with the z axis?
- The position of a particle is defined byr = {20 cos t i+ 8 sint j}m, where t is in seconds and the arguments for the sine and cosine are given in radians. Determine the magnitudes of the velocity and acceleration of the particle when t = 3 s.The displacement of a particle is given by s = 4t³ - 60t² + 100t -58 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 13 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 1.8 S= i fty = i ft/seca = i ft/ser sec, At t = 6.6 i S= fty = i ft/seca = i ft/se sec, Att = 9.8 sec, i fty = ft/seca = S = i ft/ser The velocity is zero when t = i sec and when t = secThe acceleration of a particle is given by a = 2t-20, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = 0 is so = -5 m, and the initial velocity is vo = 6 m/s. Once you have determined the functions of time, answer the questions. Questions: When t = 5.1 s, S= V = a = Mi MI i m m/s m/s²
- The coordinates of a particle moving along a curve are x(t) = -2t2 +15 and y(t) = t2 -10t + 15 , m whent is in seconds. Calculate the magnitude of velocity and acceleration when t= 5 sec.The acceleration as a function of time for a particle is determined to be ax(t)=Cxt2ay(t)=Cy Where Cx = 1.2 m/s4 and Cy = 2 m/s2. What is the magnitude of the average acceleration from ti = 0 seconds to tf = 5 seconds?At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive ydirection and moves in the xy plane with a constant acceleration of (2.0i - 4.0j)m/s2. At the instant the x coordinate of the particle is 15 m, what is the speedof the particle?