The position of a particle moving in a straight line is described by
x(t)=2t3−9t2+12t+5
where x is in metres and t in seconds.
a. (a) Obtain expressions for its instantaneous velocity and instantaneous acceleration.
b. (b) Calculate the numerical values of velocity and acceleration at t=2 s.
c. (c) Find the time(s) within 0 s≤t≤4 s when the particle is momentarily at rest.