Attempt following question by selecting a choice to answer.
f
The displacement function of a particle with time t in seconds is
S = 2t3 - 6t2 + 2t + 3 ft. Find the velocity of the particle when its acceleration becomes zero.
ee ffA.
f-4 ft/s
B.
f48 ft/s
C.
f3 ft/s
D.
f2 ft/s
f
A
Step 1: Here the displacement S = 2t3 - 6t2 + 2t + 2[Definition.]
Step 2: The velocity = V = dSdt
Step 3: = ddt(2t3 - 6t2 + 2t + 3)[Substitute S from step1.]
Step 4: ÞV = 6t2 - 12t + 2[Simplify.]
Step 5: The acceleration = a = dVdt[Definition.]
Step 6: = ddt (6t2 - 12t + 2)[Substitute V from step 4.]
Step 7: Þ a = 12t - 12
Step 8: Suppose a = 0 then 12t - 12 = 0 ® t = 1
Step 9: So, the acceleration of the particle is zero, at t = 1 sec.
Step 10: At t = 1 , the velocity of the particle = 6(1 )2 - 12(1 ) + 2 = -4 ft/s.