A particle moves according to a law of motionĀ sĀ =Ā f(t),Ā t ā„Ā 0, whereĀ tĀ is measured in seconds andĀ sĀ in feet.
(a) Find the velocity at timeĀ t.
(b) What is the velocity after 1 second?
(c) When is the particle at rest?
(d) When is the particle moving in a positive direction?
(e) Find the total distance travelled during the first 6 seconds.
(f) Draw a diagram like a Figure 2 to illustrate the motion of the particle.
(g) Find the acceleration at timeĀ tĀ and after 1 second.
(h) Graph the position, velocity, and acceleration functions for 0 ā¤Ā t ā¤Ā 6.
(i) When is the particle speeding up? When is it slowing down?
FIGURE 2
f(t) =Ā t3Ā ā 8t2Ā + 24t