Chapter 12, Problem 19P

The acceleration of a particle is defined by the relation a = -k√v , where k is a constant. Knowing x=0 and v=81 m/s at t=0 and v=36 m/s when x=18 m, determine: The velocity of the particle when x = 20m The time required for the particle to come to rest.

This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. In a boat race, boat A is leading boat B by 50 m and both boats are traveling at a constant speed of 207 km/h. At t = 0, the boats accelerate at constant rates. Know that when B passes A, t = 8 s and vA = 225 km/h.   Determine the acceleration of A. (You must provide an answer before moving on to the next part.)   The acceleration of A is m/s2.?   Note: please show step by step solution. Hence, double check the solution. For correction purposes!. I require  handwritten working out please!. Kindly, please meticulously, check the image for conceptual understanding and for extra information purposes!. Also on occasions, I receive wrong answers!!. Please go through the question and working out step by step when you finish them. Appreciate your time!.

The rectangular coordinates of a particle which moves with curvilinear motion are given by x = 10.75t +2.25t² - 0.45t³ and y = 6.90 + 17.43t - 2.62t², where x and y are in millimeters and the time t is in seconds, beginning from t = 0. Determine the velocity v and acceleration a of the particle when t = 8 s. Also, determine the first time that the velocity of the particle makes an angle of 30° with the positive x-axis. Answers: V = a = 17.1 10.75 i + i 5.24 i+ i 17.43 j) mm/s j) mm/s²

A car is traveling at a constant speed of 54 km/h when its driver sees a child run into the road. The driver applies her brakes until the child returns to the sidewalk and then accelerates to resume her original speed of 54 km/h; the acceleration record of the car is shown in the figure. Assuming x= 0 when t= 0, determine (a) the time t1 at which the velocity is again 54 km/h, (b) the position of the car at that time, (c) the average velocity of the car during the interval 1 s ≤ t≤ t1.

The acceleration of a particle is defined by the relation a = k (1 - ex), where k is a constant. The velocity of the particle is v= +9 m/s when x=- 3 m and it comes to rest at the origin. Determine the value of k. (You must provide an answer before moving on to the next part.) m²/s2. The value of k is

A car starts from rest at s = 0 and travels along a straight road with the speed described: t = 0 s, v = 0 m/s; t = 4 s, v = 5 m/s; t = 10 s, v = 5 m/s; t = 15 s, v = 0 m/s. Determine the total distance the car travels until it stops.

The acceleration of a particle is defined by the equation a = -k/x. When x = 0.9 ft, v = 12 mph. When x = 1.8 ft, v = 11 kph. Determine (a) the velocity of the particle when x = 24 in, (b) the position of the particle when v = 0.

4. A particle moves along a horizontal path with its velocity varying with time as shown. The average acceleration of the particle is a. 0.4 m/s² b. 0.4 m/s² - c. 1.6 m/s² d. 1.6 m/s² 3 m/s t=2s 5 m/s t=7s 5. A particle has an initial velocity of 30 ft/s to the left. If it then passes through the same location 5 seconds later with a velocity of 50 ft/s to the right, the average velocity of the particle during the 5 s time interval is a. 10 ft/s → b. 40 ft/s → c. 16 ft/s → d. 0 ft/s

A subway car leaves station A; it gains speed at the rate of 4 ft/s² for 6 s and then at the rate of 6 ft/s² until it has reached the speed of 48 ft/s. The car maintains the same speed until it approaches station B; brakes are then applied, giving the car a constant deceleration and bringing it to a stop in 6 s. The total running time from A to B is 40 s. Determine the distance between stations A and B. . Do not type the solution. Show the complete computation/solution with the necessary graphs or diagrams.