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Worksheet: Newton's Second Law of Motion in Vector Notation

Q1:

If a body of mass 1 kg moves under the action of forces and , what is its acceleration?

  • A m/s2
  • B m/s2
  • C m/s2
  • D m/s2

Q2:

A body of mass 11 kg is moving such that the horizontal and vertical components of its velocity are given by 𝑣 = 4 π‘₯ and 𝑣 = βˆ’ 9 . 8 𝑑 + 1 2 𝑦 where 𝑣 π‘₯ and 𝑣 𝑦 are measured in meters per second. Find the force F , in newtons, that is acting on the body during its motion and the body’s initial speed 𝑣 0 .

  • A 𝑣 = 4 √ 1 0 / 0 m s , F j = βˆ’ 2 3 9 . 8
  • B 𝑣 = 4 / 0 m s , F i j = 4 βˆ’ 1 0 7 . 8
  • C 𝑣 = 4 / 0 m s , F i j = 4 + 2 4 . 2
  • D 𝑣 = 4 √ 1 0 / 0 m s , F j = βˆ’ 1 0 7 . 8

Q3:

A particle of unit mass was moving under the effect of three forces: , , and , where and are two perpendicular unit vectors and and are constants. If the displacement vector of the particle as a function of the time is given by , find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q4:

Given that the motion of a body of mass 2 kg is represented by the relation r c ( 𝑑 ) = ο€Ή 6 𝑑 + 1 5 𝑑 + 2  2 , where c is a constant unit vector, r is measured in meters, and 𝑑 is measured in seconds, determine the magnitude of the force acting on the body.

  • A 28 N
  • B 54 N
  • C 12 N
  • D 24 N

Q5:

A particle of mass 5 kg was in motion. The components of its velocity in the horizontal and vertical directions were and , respectively. Determine the magnitude, , and direction, , of its initial velocity and the force acting on it.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q6:

A particle of unit mass is moving such that its velocity at a given time is represented by , where is a constant unit vector. Given that the force acting on the particle at time is , find and .

  • A ,
  • B ,
  • C ,
  • D ,

Q7:

A body of mass 478 g has an acceleration of m/s2, where and are perpendicular unit vectors. What is the magnitude of the force acting on the body?

Q8:

A particle of mass π‘š kg is moving under the action of two forces: F i j 1 = 8 π‘š + 6 π‘š and F i 2 = 4 π‘š , where i and j are two perpendicular unit vectors. Find the acceleration a of the particle and its magnitude | | a in meters per second squared.

  • A a i j = 1 2 βˆ’ 6 , | | = 6 √ 5 / a m s 2
  • B a i j = 4 + 6 , | | = 2 √ 1 3 / a m s 2
  • C a i j = 1 2 + 6 , | | = 6 √ 3 / a m s 2
  • D a i j = 1 2 + 6 , | | = 6 √ 5 / a m s 2

Q9:

A particle of unit mass is moving along a certain path, where its velocity at time is given by the relation , where is a constant unit vector. Given that the force acting on the particle is constant and given by the relation , determine the values of the constants and .

  • A ,
  • B ,
  • C ,
  • D ,

Q10:

A body of mass is moving under the action of a force . Its velocity at time seconds is given by the relation , where is a unit vector in the direction of its motion, and and are constants. Given that the initial velocity of the body and , find the body’s velocity at seconds.

Q11:

A body of mass 9 g was moving on a plane under the effect of the force dynes. Given that the position vector of the body is given by the relation , determine and .

  • A ,
  • B ,
  • C ,
  • D ,

Q12:

A body of mass 250 g moves under the action of a force, newtons. Given that the body starts from rest at the origin, and , where and are perpendicular unit vectors, find the displacement in terms of .

  • A
  • B
  • C
  • D

Q13:

A body of mass 7 kg moves under the action of three forces, , , and . Given that the displacement of the particle at time seconds is , determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q14:

A body of mass 1 kg was moving in a straight line with a velocity , where and are two perpendicular unit vectors. The force acted on the body for 8 seconds. Find the body’s speed after the action of this force.

  • A m/s
  • B m/s
  • C 40 m/s
  • D m/s

Q15:

A body of mass 3 units was moving under the action of two coplanar forces and such that and , where and are two perpendicular unit vectors. Given that the acceleration of the body is , find the values of the constants and .

  • A ,
  • B ,
  • C ,
  • D ,

Q16:

A body of mass 2 kg moves in a horizontal plane in which and are perpendicular unit vectors. At time seconds , the force acting on the particle is given by . Find the speed of the body, , and its distance from the origin, , when .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q17:

If the forces N and acting on a body of mass 6 kg, cause an acceleration , what are the values of , , and ?

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q18:

Three forces, , , and , where , , and are three perpendicular unit vectors, are acting upon a body of unit mass. If the displacement vector of the particle is , determine the constants , , and .

  • A , , and
  • B , , and
  • C , , and
  • D , , and
  • E , , and

Q19:

A body of unit mass was moving under the effect of a force , where and are two orthogonal unit vectors. If the displacement vector of the body at time is given by , find and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,