Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Finding the Acceleration Vector by Differentiation

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 ) = ( 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
  • B 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
  • C 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
  • D 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
  • E 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

Q2:

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

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