The rectangular coordinates of a particle which moves with curvilinear motion are given by x= 9.75t+2.50t² -0.40t³ and y = 5.45 +25.04t - 3.31t², 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 = 7 s. Also, determine the first time that the velocity of the particle makes an angle of 28° with the positive x-axis. Answers: v = (i a = (i t= i i+i i+ i S j) mm/s j) mm/s²

a_av = 3.9051 m/s^2

The y-coordinate of a particle in curvilinear motion is given by y = 9.0t³ - 13.3t, where y is in inches and t is in seconds. Also, the particle has an acceleration in the x-direction given by ax = 4.3t in./sec². If the velocity of the particle in the x-direction is 12.1 in./sec when t = 0, calculate the magnitudes of the velocity v and acceleration a of the particle when t = 3.2 sec. Construct v and a in your solution. Answers: When t = 3.2 sec, V = i in./sec a = in./sec² Mo

Situation 3: The speed of the train during the first minute has been recorded as follows: t(s) 0 40 60 80 v (m/s) 0 20 25 34 Plot the v-t graph, approximating the curve as straight-line segments between the given points. Determine the total distance traveled.

At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.78i m. By time t = 0.019 s, its position vector has become (4.96i + 0.52j) m. Determine the magnitude Vay of its average velocity during this interval and the angle e made by the average velocity with the positive x- axis. Answers: Vav Ꮎ = = i i m/s

A car is travelling at vo = 21 m/s when a passing obstruction is sighted ahead at 120 m. The driver decelerates constantly at 4 m/s² until it is 70 m away from the former location of the obstruction, then accelerates at 3 m/s² for 15 seconds. 1. Find the total distance travelled by the car for the whole duration. m use 2 decimal places m/s use 2. Find the speed when it is 70 m away from the obstruction. 2 decimal places 3. Find the final speed. m/s use 2 decimal places

Need help. Thank you

2/137 The curvilinear motion of a particle is governed by the polar coordinates r = t³/3 and 0 = 2 cos (nt/6), where r is in meters, is in radians, and t is in seconds. Specify the velocity v and acceleration a of the particle when t = 2 s. Ans. v = 4e, a = 2.42e, m/s 1.807e, 7.99e, m/s² -

9. The helicopter is tracked by radar, which records R, 0, and è at regular time intervals. The readings at a certain instant are R = 2500 m, 0 = 40°, and 0 = 0.04 rad/s. If the helicopter is in level flight, calculate the elevation O of the helicopter in m at this instant.