Worksheet: The Net Change Theorem

In this worksheet, we will practice applying the net change theorem.

Q1:

True or False? The Net Change Theorem says that ο„Έ √ π‘₯ π‘₯ = √ 9 βˆ’ √ 4  οŠͺ d .

  • Atrue
  • Bfalse

Q2:

True or False: If 𝑔 ( 𝑑 ) represents the rate of change of a cat’s weight in kilograms per month when it is 𝑑 months old, then ο„Έ 𝑔 ( 𝑑 ) 𝑑 οŠͺ  d equals the cat’s weight when it is 4 months old.

  • Afalse
  • Btrue

Q3:

True or False: The net change theorem states that ο„Έ π‘₯ √ 𝑑 𝑑 = √ π‘₯ βˆ’ √ π‘Ž   d d d .

  • AFalse
  • BTrue

Q4:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 5 𝑑 βˆ’ 3  . What distance does it travel between 𝑑 = 2 and 𝑑 = 4 ?

  • A 31 m
  • B 2 m
  • C 4 3 m
  • D 7 m

Q5:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 5 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 1 ?

  • A 1 3 1 0 m
  • B 7 1 0 m
  • C 1 1 0 m
  • D 2 m
  • E 1 2 m

Q6:

Suppose that 𝐹 ( 𝑑 ) = 𝑑  . Evaluate ο„Έ 𝐹 β€² ( 𝑑 ) 𝑑   d using the net change theorem.

Q7:

An oil tanker leaks at the rate π‘Ÿ = 𝑓 ( 𝑑 ) liters per minute, where 𝑑 is the number of minutes after the accident. Write an integral that expresses the volume of oil leaked out in the first hour.

  • A ο„Έ 𝑓 ( 𝑑 ) 𝑑   d
  • B ο„Έ 𝑓 β€² ( 𝑑 ) 𝑑    d
  • C ο„Έ 𝑓 β€² ( 𝑑 ) 𝑑    d
  • D ο„Έ 𝑓 β€² ( 𝑑 ) 𝑑   d
  • E ο„Έ 𝑓 ( 𝑑 ) 𝑑    d

Q8:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 𝑑 βˆ’ 4 𝑑 + 3  . What distance does it travel between 𝑑 = 2 and 𝑑 = 5 ?

  • A 1 3 3 m
  • B 60 m
  • C 6 m
  • D 2 2 3 m
  • E 4 4 3 m

Q9:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 𝑑 βˆ’ 2 𝑑 βˆ’ 3  . What distance does it travel between 𝑑 = 1 and 𝑑 = 4 ?

  • A 15 m
  • B 2 3 3 m
  • C 2 6 3 m
  • D 1 4 3 m
  • E 3 m

Q10:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 4 𝑑 βˆ’ 1 . What distance does it travel between 𝑑 = 0 and 𝑑 = 2 ?

  • A 6 m
  • B 2 5 4 m
  • C 3 2 m
  • D 3 1 4 m
  • E 14 m

Q11:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 5 ?

  • A 4 1 2 m
  • B 10 m
  • C 35 m
  • D 2 9 2 m
  • E 4 m

Q12:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 4 ?

  • A 20 m
  • B 2 3 2 m
  • C 1 7 2 m
  • D 4 m
  • E 2 m

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