The position of a particle moving along an `x` axis is given by `x=12t^(2)-2t^(3)`, where `x` is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at `t=3.5s`. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached ? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached ? (h) What is the acceleration of the particle at the instant the particle is not moving ( other than at `t=0` ) ? (i) Determine the average velocity of the particle between `t=0` and `t=3`s .

Answer

(a) 61 m; (b) 11 m/s; (c) `-18 m//s^(2)`; (d) `x=64 m`; (e) 4.0 s; (f) 24 m/s; (g) 2.0 s; (h) `-24 m//s^(2)`; (i) 18 m/s