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The position of a particle along a straight line is given by s= t^3 −9t^2 + 15t [ft] where t
is in seconds. Find average speed, average velocity, acceleration, displacement, distance traveled, and at what time did the direction reverse.
0 ≤ t ≤10 [s]
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- Your answer is partially correct. Raindrops fall 1.46 × 10° m from a cloud to the ground. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Number i Units m/sSolve the following two equations for the (positive) time, t, and the position, x. Assume SI units. x = 3.00t2 and x = 45.0t + 63.0 (b) the position, xmAnswers should be in 3 decimal places. A particle moves along a straight line in such a manner that its displacement, at any instant, from a fixed point on its path is given by the equation s = (t3 + 6t2 – 4t)/10. Determine the distance (in meter) traveled by the particle during the 10th sec.
- The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.A particle moves along two dimensions based on the following position vector r= [2.0 m + (3.00 m/s)f ]i + [(3.0 m)t - (2.00 m/s2)rlj a. Find the distance it covered in the first minute. b. Find the general expression of the instantaneous acceleration of the particle.Solve the following two equations for the (positive) time, t, and the position, x. Assume SI units. x = 3.00t2 and x = 45.0t + 63.0 (a) the (positive) time, t
- Ajetliner, traveling northward, is landing with a speed of 68.2 m/s. Once the jet touches down, it has 750 m of runway in which to reduce its speed to 7.16 m/s. Compute the average acceleration (magnitude and direction) of the plane during landing (take the direction of the plane's motion as positive). Number i Units 4The displacement of a particle is given by s = 2t3 - 32t2 + 89t - 32 where s is in feet and tis 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: Att= 2.9 sec, ft, v= i ft/sec, a = i ft/sec2 At t = 6.3 sec, i ft. v= ft/sec, a = i ft/sec? At t = 11.6 i ft. v= ft/sec, a = i ft/sec2 sec, The velocity is zero when t = i sec and whent= i secProblem 5. The velocity of a particle moving along the x -axis is defined by v = kx°- 4x² + 6x , where v is in m/sec, x in meters , and k is constant. If K = 1, compute the value of acceleration after x= 2meters. Find: 10. a = ?
- The displacement of a particle is given by s = 3t3 - 42t2 + 109t - 39 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 11 seconds of motion. After you have made the plots, answer the questions. Questions: Att = 2.4 ft. v= ft/sec. a = ft/sec? sec, Att= 5.4 i ft, v= i ft/sec, a = i ft/sec? S= sec, Att = 8.5 ft. v= i ft/sec, a = i ft/sec? sec, The velocity is zero when t = i sec and when t = i secThe 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 = secThe speed (m/s) an accelerating object is traveling is determined by the function v(d) = 9.8d + 8 where d is the distance the car has been accelerating. How fast (m/s) is the object traveling after 20 meters? Leave your answer without writing the units. 204