# Linear Motion in Engineering Mechanics

## Linear Motion:

A body is said to be at rest, if it occupies the same position with respect to its surroundings at all moments. But it is said to be in motion, if it changes its position, with respect to its surroundings. Linear Motion is a one dimensional motion that takes place in a straight line. The linear motion can be of two types:

• Uniform linear motion
• Non-Uniform linear motion

Example: A train running on a track
.

## Important Terms on Linear Motion:

1. Speed: The speed of a body may be defined as its rate of change of displacement with respect to its surroundings. The speed of a body is irrespective of its direction and is thus a scalar quantity.

2. Velocity: The velocity of a body may be defined as its rate of change of displacement with respect to its surroundings in a particular direction. As the velocity is always expressed in particular direction, therefore it is a vector quantity.

3. Acceleration: The acceleration of a body may be defined as the rate of change of its velocity. It is said to be positive, when the velocity of a body increases with time and negative when the velocity decreases with time. The negative acceleration is also called retardation. In general, the term acceleration is used to denote the rate at which the velocity is changing. It may be uniform or variable.

4. Uniform Acceleration: If a body moves in such a way that its velocity changes in equal magnitudes in equal intervals of time. It is said to be moving with a uniform acceleration.

5. Variable Acceleration: If a body moves in a such a way that its velocity changes in unequal magnitudes in equal intervals of time. It is said to be moving with a variable acceleration.

6. Distance Traversed: It is the total distance moved by a body. Mathematically, if a body is moving with a uniform velocity (v), then in t seconds, the distance traversed.

s = vt