Question

A particle moves along a line so that its position at any time is t>0 or t=0 is given by the function s(t)=(t^3)-(6t^2)+(8t)+2 where s is measured in meters and t is measured in seconds. a) find instantaneous velocity at any time t. b) find acceleration of the particle at any time t. c) when is the particle at rest?. d) describe motion of the particle. at what values of t does the particle change directions

Answer 1

a. The instantaneous velocity at any time is  3t^2 -12t +8.
b. The acceleration of the particle at any time is 6t - 12.
c. The acceleration when particle is at rest is 3t^2 -12t+8 = 0.
d. The particle travels like a cubic graph.