The motion of a particle is defined by the relation x=2t^ 3 -9t^ 2 +12t+10. where x and I are expressed in feet and seconds, respectively. Determine the time, the position, and the acceleration of the particle when v = 0

A particle is observed to start at rest and acceleration at a=30+2t, where t is in seconds, until its velocity is 39.20 m/s. It then hits an obstruction and the acceleration is given by a= -0.003v2, until the velocity decreases to 98.20 m/s. Determine the total distance the particle travelled, and the total time of travel.

2/2 The displacement of a particle is given by s = 30t2 + 100t – 50, where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as 213 – - functions of time for the first 12 seconds of motion. Determine the time at which the velocity is zero.

Specifically a dynamics of a particle question: The acceleration of a particle as it moves along a straight line is given by a = (2t - 1) m/s2. If s = 1 m and v = 2 m/s when t = 0, determine the particle's velocity and position when t = 6 s. Also determine the total distance the particle travels during this time period.