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Question

 A particle moves according to the law of motion 𝑠(𝑡)=𝑡3−8𝑡2+3𝑡s(t)=t3−8t2+3t, 𝑡≥0t≥0, where 𝑡t is measured in seconds and 𝑠s in feet. 

a.) Find the velocity at time 𝑡t. 

Answer:  

b.) What is the velocity after 33 seconds? 

Answer:  

c.) When is the particle at rest? Enter your answer as a comma separated list. Enter None if the particle is never at rest. 

At t₁ =___and t₂= ___ with 𝑡1<𝑡2

d.) When is the particle moving in the positive direction? 

When 0≤𝑡< ____  and 𝑡> ______

Answer 1

 A particle moves according to the law of motion 𝑠(𝑡)=𝑡3−8𝑡2+3𝑡s(t)=t3−8t2+3t, 𝑡≥0t≥0, where 𝑡t is measured in seconds and 𝑠s in feet. 

a.) Find the velocity at time 𝑡t. 

Answer:   Velocity = derivative,

so velocity = s'(t) = 3t² - 16t + 3

b.) What is the velocity after 33 seconds? 

Answer:   s'(33) = 3(33)² -16(33) + 3 = 2742 ft/sec

c.) When is the particle at rest? Enter your answer as a comma separated list. Enter None if the particle is never at rest. 

rest = when velocity = 0

s'(t) = 3t² - 16t + 3 = 0

t = .1946 and 5.1387 sec

At t₁ =___and t₂= ___ with 𝑡1<𝑡2

d.) When is the particle moving in the positive direction? 

3t² - 16t + 3 > 0 (note this is a parabola that open up, so the parts ABOVE x axis are the left and right branches on either side of the zeros)

When 0≤𝑡< .1946  and 𝑡> 5.1387