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Worksheet: Finding Momentum Using Vectors

Q1:

A body of mass 7 kg is moving in a straight line. Its position vector at a time 𝑑 is given by the relation r i j ( 𝑑 ) = ο€Ή 𝑑 + 5  + ο€Ή 𝑑 + 𝑑  2 3 , where | | r is measured in meters and 𝑑 in seconds. Determine the body’s momentum after 2 seconds.

  • A 5 6 + 8 4 i j
  • B 2 8 + 8 5 i j
  • C 1 4 + 1 3 i j
  • D 2 8 + 9 1 i j

Q2:

A body with variable mass moves in a straight line. At time 𝑑 seconds, its mass is given by π‘š = 7 ( 𝑑 + 4 ) k g , and its displacement from a fixed point on the line is given by 𝑠 = 1 4 ο€Ή 𝑑 βˆ’ 2 𝑑 + 1 0  2 m . Calculate the change in the body’s momentum between 𝑑 = 1 0 s and 𝑑 = 1 3 s .

  • A 686 kgβ‹…m/s
  • B 49 kgβ‹…m/s
  • C 196 kgβ‹…m/s
  • D 273 kgβ‹…m/s

Q3:

A body of mass 3 kg is moving in a straight line. Its position vector at a time 𝑑 is given by the relation r i j ( 𝑑 ) = ο€Ή 𝑑 + 5  + ο€Ή 𝑑 + 𝑑  2 3 , where | | r is measured in meters and 𝑑 in seconds. Determine the body’s momentum after 3 seconds.

  • A 5 4 + 8 1 i j
  • B 1 8 + 8 2 i j
  • C 9 + 2 8 i j
  • D 1 8 + 8 4 i j

Q4:

A body of variable mass is moving along a fixed straight line. Its mass at time is given by the relation and its displacement is given by the relation , where is a unit vector parallel to the direction of its motion. Determine the body’s momentum and the force that is acting on it .

  • A ,
  • B ,
  • C ,
  • D ,

Q5:

Determine the mass of a body whose momentum is 37 kgβ‹…m/s, given that its displacement vector is given by the relation s i j ( 𝑑 ) = ( βˆ’ 3 𝑑 ) + ( 4 𝑑 ) , where | | s is measured in meters and 𝑑 in seconds.

  • A 1 480 g
  • B 3 700 g
  • C 185 g
  • D 7 400 g