A material point moves with an acceleration a(t) = 2ti + 2sintj - costk At time t=0 the particle is at position ro(t) = 3i - 3j and has speed uo(t) = 2j + k. Find the velocity u(t)and the position r(t).
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- A If the vector components of a particles position moving in the xy plane as a function of time are x=bt2i and y=ct3j, where b and c are positive constants with the appropriate dimensions such that the components will be in meters, at what time t is the angle between the particles velocity and the x axis equal to 45?Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 45 with respect to the 50-yard line and covers 8.0 m in 1 s. He then fins straight down the field at 90 with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews’ final displacement from the start of the play? (b) What is his average velocity?Problems 3 and 12 are paired. G A particle moves from position A to position C as shown in Figure P2.3. Two different coordinate systems have been chosen. Write expressions for the particle at all three positions using a. the top coordinate system, and b. the bottom coordinate system. FIGURE P2.3 Problems 3 and 12.
- Pete and Sue, two reckless teenage drivers, are racing eastward along a straight stretch of highway. Pete is traveling at 98.0 km/h, and Sue is chasing him at 125 km/h. a. What is Petes velocity with respect to Sue? b. What is Sues velocity with respect to Pete? c. If Sue is initially 325 m behind Pete, how long will it take her to catch up to him?A. Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) = (t?)i + (t+)j+ (t-) k in the form a(t) = ar T + ay N at the value of t = 1.A particle moves in the x-y plane, starting from the origin with an initial velocity of ( 4i -8.7j) m/s. The particle experiences a constant acceleration of ( 4i ) m/s?. Calculate the speed of the particle at t = 5 s а. 99.69 b. 24.18 O' c. 584.70 d. 25.53
- At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (2.0 i - 4.0 j) m/s 2. At the instant the x coordinate of the particle is 15 m, what is the speed of the particle? O a. 14 m/s O b. 12 m/s O c. 16 m/s O d. 10 m/s O e. 26 m/sA car's velocity is at 100 km/h going North [N] for 1.0 hour. The car continues to move for another 2.0 hours at 82 km/h South [S). Determine the car's: A trekker walks 5.0 km North [N] and then 8.0 km South [S] for 3.0 hours. Let's Appraise 1. Determine the trekker's: Average velocity а. b. Average speed 2. Total displacement a. b. Moving average velocity C. Total distance covered d. Moving average speed Plot a graph using the values given in the table of distance and time 3. Determine the moving average velocity during the first 5.0 seconds. а. t(s) d(m) 0.5 0.5 Determine the moving average velocity during the time interval of 2.0 to 13.0 seconds. b. 1.0 1.2 1.5 2.0 2.0 3.0 Determine the time if the 2.5 4.1 С. velocity is zero, 3.0 5.3 3.5 6.9 d. Determine the velocity for each given time: 4.0 8.7 4.5 10.7 i. 3.0 s 5.0 13.0 5.5 15.0 ii. 6.5 s 6.0 16.1 iii. 11.0 s 6.5 16.9 7.0 17.3 7.5 17.8 8.0 17.9 8.5 18.0 9.0 18.0 17.8 17.6 9.5 10.0 10.5 17.2 11.0 16.8 11.5 16.3 15.7 14.9 12.0 12.5…An object is released from rest at a height of h. During the final second of its fall, it traverses a distance of 38m. Determine h. I would like to know the solution but also maybe an explanation on how I would know what process to take. For the last second, I was able to find that final vf = 38m/s. That is vf = deltax/deltat, or 38m/1s. I plugged it in to vf2 = vo2 + 2a(deltax), since I think that vf shouldn't change for h, but I got the wrong answer. Please explain.
- A rabbit runs across a parking lot on which a set of coordinate axis has been drawn. The coordinates of the rabbit’s position as a function of time t are given by: x = -0.3t2 + 5t + 28 and y = 0.22t2 - 8t + 30 with t in seconds and x and y in meters. What is the velocity at t= 10 sec? A. 0.6 i + 0.4 j B. -0.2i +1.6j +30 C. -i - 3.6 j D. 4i + 2jGiven that r (t) = (3t cos t)j – (3t sin t) k , is the position В. vector of a moving particle, find the following quantities: 1. The velocity, speed, acceleration, and curvature of the particle, 2. The tangential and normal components of acceleration of the particle. B.s on A runner is also on the track going in the same direction as the walker, running at an unknown constant speed. The runner and the walker are together, then meet each other again when the walker has completed 1/2 of a lap, or 200m. What is the runner's speed? A walker is walking at a constant rate of 1 m/s on a circular track that is 400 m in length.