Dynamics-

1. A particle travels along a straight line with a velocity v = (12 - 3t²) m/s, where t is in seconds. When t = 1 s. the particle is located 10 m to the left of the origin. Determine the acceleration when t= 4 s, the displacement from t = 0 to t = 10 5, and the distance the particle travels during this time period.

2. The acceleration of a particle as it moves along a straight line is given by a = (2t - 1) m/s², where t is in seconds. If s = 1 m and v = 2 m/s when t = O. determine the particle's velocity and position when t = 6 s. Also, determine the total distance the particle travels during this time period.

3. The position of a particle along a straight-line path is defined by s = (t³ - 6t² - 15t + 7) ft, where t is in seconds. Determine the total distance traveled when t = 10 s. What are the particle's average velocity, average speed, and the instantaneous velocity and acceleration at this time?

4. A train starts from rest at station A and accelerates at 0.5 m/s² for 60 s. Afterwards it travels with a constant velocity for 15 min. It then decelerates at 1 ms² until it is brought to rest at station B. Determine the distance between the stations.

5. A particle is moving along a straight line such that its acceleration is defined as a = (-2v) m/s². where v is in meters per second. If v = 20 m/s when s = 0 and t = 0, determine the particle's position, velocity, and acceleration as functions of time.

6. Two particles A and B start from rest at the origin s = 0 and move along a straight line such that a_A = (6t - 3) ft/s² and a_B = (12t² - 8) ft s², where t is in seconds. Determine the distance between them when t = 4 s and the total distance each has traveled in t = 4 s.