A particle moves according to a law of motion s 14 t4 2t3

A particle moves according to a law of motion s = 14 t4 - 2t3 + 11/2t2 - 6t + 2, t is in seconds and s is in feet Find the velocity at time t. What is the velocity after 2 s? When is the particle at rest? When is the particle moving to the left/right? Find the total distance traveled in the first 4 seconds (pay attention to when the particle stopped). Draw a diagram to illustrate the motion of the particle.

Solution

s = 1/4t^4 -2 t^3 +11/2 t^2 -6t +2 a.ds/dt = v = t^3 -6t^2 + 11t -6 b.v at 2 sec = 0 c.at t = 2 s d.t>6s e.26.4m