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Lesson: Finding the Acceleration Vector by Differentiation

Sample Question Videos

Worksheet • 2 Questions • 1 Video

Q1:

Find the velocity 𝑣 ( 𝑑 ) and acceleration π‘Ž ( 𝑑 ) of an object with the given position vector π‘Ÿ ( 𝑑 ) = ( 3 𝑑 , 2 𝑑 , 1 ) c o s s i n .

  • A 𝑣 ( 𝑑 ) = ( βˆ’ 3 𝑑 , 2 𝑑 , 0 ) s i n c o s , π‘Ž ( 𝑑 ) = ( βˆ’ 3 𝑑 , βˆ’ 2 𝑑 , 0 ) c o s s i n
  • B 𝑣 ( 𝑑 ) = ( βˆ’ 3 𝑑 , 2 𝑑 , 1 ) s i n c o s , π‘Ž ( 𝑑 ) = ( βˆ’ 3 𝑑 , βˆ’ 2 𝑑 , 1 ) c o s s i n
  • C 𝑣 ( 𝑑 ) = ( 3 𝑑 , βˆ’ 2 𝑑 , 0 ) s i n c o s , π‘Ž ( 𝑑 ) = ( 3 𝑑 , 2 𝑑 , 0 ) c o s s i n
  • D 𝑣 ( 𝑑 ) = ( βˆ’ 3 𝑑 , βˆ’ 2 𝑑 , 0 ) s i n c o s , π‘Ž ( 𝑑 ) = ( βˆ’ 3 𝑑 , 2 𝑑 , 0 ) c o s s i n
  • E 𝑣 ( 𝑑 ) = ( 3 𝑑 , 2 𝑑 , 0 ) s i n c o s , π‘Ž ( 𝑑 ) = ( 3 𝑑 , 2 𝑑 , 0 ) c o s s i n

Q2:

Find the velocity v ( 𝑑 ) and acceleration a ( 𝑑 ) of an object with the given position vector r ( 𝑑 ) = ( 𝑑 , 𝑑 βˆ’ 𝑑 , 1 βˆ’ 𝑑 ) s i n c o s .

  • A v ( 𝑑 ) = ( 1 , 1 βˆ’ 𝑑 , 𝑑 ) c o s s i n , a ( 𝑑 ) = ( 0 , 𝑑 , 𝑑 ) s i n c o s
  • B v ( 𝑑 ) = ( 1 , 1 βˆ’ 𝑑 , 1 βˆ’ 𝑑 ) c o s s i n , a ( 𝑑 ) = ( 0 , βˆ’ 𝑑 , βˆ’ 𝑑 ) s i n c o s
  • C v ( 𝑑 ) = ( 1 , 1 βˆ’ 𝑑 , βˆ’ 𝑑 ) c o s s i n , a ( 𝑑 ) = ( 0 , 𝑑 , βˆ’ 𝑑 ) s i n c o s
  • D v ( 𝑑 ) = ( 1 , 1 βˆ’ 𝑑 , 1 + 𝑑 ) c o s s i n , a ( 𝑑 ) = ( 0 , βˆ’ 𝑑 , 𝑑 ) s i n c o s
  • E v ( 𝑑 ) = ( 1 , 1 + 𝑑 , 𝑑 ) c o s s i n , a ( 𝑑 ) = ( 1 , 𝑑 , 𝑑 ) s i n c o s
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