Starting from x= 0 with no initial velocity, a particle is given an acceleration a = 0.8 Vv² + 49, where a and vare expressed in ft/s² and f's, respectively. Required information Determine the speed of the particle when x = 42 ft. The speed is ft/s.

The acceleration of a particle traveling along a straight line is a = 1/4(s^1/2 )m/s^2, where s is in meters. If v = 0, s = 1 m when t = 0, determine the particle’s velocity at s = 2 m.

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.

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.