The motion of a particle is defined by the relation x=3t³-6t²-12t+5, where x and t are expressed in m and sec, respectively. Determine the average acceleration during the time interval 1 ≤ t ≤ 4.

The acceleration of a particle moving horizontally under rectilinear motion is defined by the relation  a=8.9t2-5.1t where a is in ft/s2 and t is in s. Initially, the particle is at rest and started at x=14.3 ft. Determine the position of the particle at t=4.3s. Round off only on the final answer expressed in 3 decimals. Indicate appropriate units.

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.