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

In this worksheet, we will practice applying Newton’s second law when the forces acting on a body and the motion caused by them are represented in the vector notation.

**Q2: **

A body of mass 11 kg is moving such that the horizontal and vertical components of its velocity are given by and where and are measured in metres per second. Find the force , in newtons, that is acting on the body during its motion and the body’s initial speed .

- A ,
- B ,
- C ,
- D ,

**Q3: **

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 ,

**Q4: **

A particle of mass kg is moving under the action of two forces: and , where and are two perpendicular unit vectors. Find the acceleration of the particle and its magnitude in metres per second squared.

- A ,
- B ,
- C ,
- D ,

**Q5: **

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 , ,

**Q6: **

Given that the motion of a body of mass 2 kg is represented by the relation , where is a constant unit vector, is measured in metres, and is measured in seconds, determine the magnitude of the force acting on the body.

**Q7: **

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 ,

**Q8: **

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 ,

**Q9: **

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 ,

**Q10: **

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

- A ,
- B ,
- C ,
- D ,

**Q11: **

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 ,

**Q12: **

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 ,

**Q13: **

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

**Q14: **

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 , ,

**Q15: **

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 speed at .

**Q16: **

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

**Q17: **

A body of mass 478 g has an acceleration of
m/s^{2}, where
and
are perpendicular unit vectors. What is the magnitude of the force acting on the
body?

**Q18: **

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

**Q19: **

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 ,