* Motion as a Mechanical Engineering Project* is movement of an object in certain planes. Motion as a Mechanical Engineering Project can be in one, two or three dimensions.

# Motion as a Mechanical Engineering Project; One Dimension

One dimension in motion means that the body is moving in only one plane and that therefore implies that the body moves in a straight line. If one rolls a marble on a flat surface and in a straight line (not easily done), the marble would be undergoing one dimensional motion as defined in Motion as a Mechanical Engineering Project.

Ther

e are four acute variables which when put together in an equation describe one dimensional motion. These are;

- Acceleration (a)
- Velocity (V);
- Initial velocity (u)
- Final Velocity (v)
- Displacement (s) and
- Time elapsed (t).

The equations below show the relationship between these variables in one dimensional motion;

- V2 = u2 + 2as
- V = u + at
- S = ut + 1/2 at2
- Average velocity = (v + u)/ 2

With these equations found in Motion as a Mechanical Engineering Project, one can calculate on any form of motion in a straight e.g. the acceleration of a car.

## Motion as a Mechanical Engineering Project; Two & Three Dimensions

The two forms of dimensional motion in the Motion as a Mechanical Engineering Project are better defined when divided into scalar and vector quantities. The difference between scalar and vector quantities as put in Motion as a Mechanical Engineering Project is in the terms ‘magnitude’ and ‘direction’. Magnitude defines how much of the quantity is there. Direction is the way in which a certain magnitude moves. Scalars are physical quantities which are defined by their magnitude only. Scalars include mass, speed, volume, distance etc. Vectors are physical quantities defined by their magnitude and direction. Vectors include velocity, acceleration, force, momentum etc in Motion as a Mechanical Engineering Project.

**Motion as a Mechanical Engineering Project; Vector Addition **

*Resolution of vectors in Motion as a Mechanical Engineering Project*

Vectors as defined in Motion as a Mechanical Engineering Project have components, and it is often advisable to split a vector into its components. The splitting of a vector into its constituent components is what is termed as the resolution of the vector. The initial vector forms as a the resultant of these components. When the vector components are perpendicular to each other, they are named the rectangular components of a vector.

*Parallelogram law of vector addition in Motion as a Mechanical Engineering Project*

If one was to represent two vector quantities using the two adjacent sides of a parallelogram, the diagonal joining the two ends of the initial vectors becomes the resultant vector. The resultant vector combines the effects of the two initial vectors.

*Rectangular Components of a Vector in Motion as a Mechanical Engineering Project*

With the components of the vector at right angles, one can do mathematics on them as in Motion as a Mechanical Engineering Project, it allows for the solving of many life problems. After all, the best part about physics is that it can be employed to solve real world issues/problems. Since it is hard to use vector notations on computer, we shall use bold letters to denote vector quantities and normal letters to denote scalar quantities. Subscripts of ‘x’ and ‘y’ will be used to show that the motion is either along the x or the y axes.

Let **A**_{x} and **A**_{y} be the rectangular components of the vector **A**

Then; A = **A**_{x }+ **A**_{y}** **

This shows that the vector **A** is the resultant vector of vectors **A**_{x} and **A**_{y}, and **A**_{x} and **A**_{y} are the components.A is the magnitude of the vector **A** and similarly, the A_{x} and A_{y} are the magnitudes of the vectors **A _{x}** and

**A**. We can therefore say that:

_{y}A = √(A_{x} + A_{y})

Given that the angle made by the vector **A **and the x axis is Q;

Q = tan^{-1} (A_{x} / A_{y})

## Laws of Motion in Motion as a Mechanical Engineering Project

**The first law in Newton’s Laws of Motion**

The law in Motion as a Mechanical Engineering Project** is** stated as follows: – a body tends to remain at rest or in uniform motion in a straight line (with constant velocity) unless acted upon by a resultant force. The tendency of a body to continue in its initial state of motion (a state of rest or a state of uniform motion in a straight line) is called inertia in Newton’s Laws of Motion.

**The second law in Newton’s Laws of Motion**

The law in the Motion as decribed in a Mechanical Engineering Project** is **stated as described below: – if a net force acts on a body, it will cause an acceleration of that body. That acceleration in the direction of the net force and its magnitude is proportional to the magnitude of the net force and the inversely proportional to the mass of the body i.e.

**a** α **F**/m, so that **F** = km**a**.

This vector equation is a relation between vector quantities **F** and **a** and thus applies to the x, y and z planes of the Cartesian plane. Motion defined by the three planes of the Cartesian plane is termed as three dimensional in Motion as a Mechanical Engineering Project**.**

**The third law in Newton’s Laws of Motion**

The law in Motion as a Mechanical Engineering Project** is** stated as follows: – action and reaction forces are always equal and opposite i.e. when a body in Newton’s Laws of Motion exerts a force on another, the second exerts an equal, oppositely directed force on the first. I.e.

**F **α** R**

### Conclusion on Motion as a Mechanical Engineering Project

The third law in Newton’s Laws of Motion however differs from the first and the second in that; whereas the first and second laws in Newton’s Laws of Motion are concerned with the behaviors of a single body, the third law in Newton’s Laws of Motion is concerned with two separate bodies. The inherent symmetry of the action-reaction couple precludes identifying one as action and other as reaction in **Motion as a Mechanical Engineering Project****.**