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# Rectilinear Motion

## What is Rectilinear Motion?

Rectilinear Motion is a type of motion that occurs only along one axis or direction. It is also referred to as linear motion. Let us now learn about the meaning, definition, types, some examples, and physical quantities or parameters of rectilinear motion.

### Introduction

We already know about motion, the most common phenomenon in our daily life. A body is considered to be in motion if its position changes with time. Motion is characterized mathematically by quantities like displacement, velocity, and acceleration in relation to a certain frame of reference.

Depending on the particle’s path, the motion can be of several forms, such as translational motion, rectilinear motion, curvilinear motion, and so on. Out of these different types of motions, rectilinear motion is the most basic one.

### Rectilinear Motion Meaning

Rectilinear Motion (also known as Linear Motion) is a type of motion. It’s a motion that has only one axis or direction. All motion parameters (distance, displacement, etc.) have one direction. Thus, the motion is referred to as one-dimensional motion.

For a particle being in rectilinear motion, it means that

• it has linear motion
• the direction of its velocity remains constant
• path of moving particle is a straight line

### Rectilinear Motion Definition

Let us now define this type of motion

Rectilinear motion is defined as motion that occor in only one direction. It’s also known as linear motion.

A free-falling object’s motion and the simple harmonic motion of a mass on a spring are examples of rectilinear motion.

### Rectilinear Motion Examples

• movement of a bullet fired from a gun
• the motion of a cyclist running on a straight road
• march past soldiers in a parade
• the motion of a vehicle on a straight road
• the motion of a falling stone
• ball rolling on the ground
• Up and down motion of elevators
• open and close movement of drawer on the table
• A train on a straight track.

It must be noted that this type of motion takes place in a fixed direction.

### Types

1. Uniform motion with no acceleration: This is a type of straight-line motion in which the moving object has a constant velocity. Because the object has a constant velocity, the motion is not accelerated. This means that the body is not subjected to any net external force.
2. Motion with non-zero constant acceleration: The velocity in this linear motion changes, while the acceleration remains constant. This means that the velocity of the moving object changes all the time, but it changes by the same amount every second.
This type of motion is explained with the help of kinematics equations of uniformly accelerated motion.
3. Motion with non-uniform acceleration: Both acceleration and velocity are not constant in this case and can vary over time.

### Physical Quantities involved

Let us now have a brief look at the physical quantities involved in this type of motion. For this, look at the figure given below that shows the linear motion of a point particle.

Here, in the above figure, $x(t)$ represents the position of the particle as a function of time (see position-time graph) in the direction of motion.

If we have knowledge about the position of the particle, we can easily calculate other kinematic variables like displacement, velocity, and acceleration.

Let us now briefly look at quantities involved in linear or straight-line motion

#### 1. Distance

The distance traveled by a moving object in a given time interval is the length of the object’s actual path between its initial and final positions.

#### 2. Displacement

Displacement is defined as a change in an object’s position. It is a vector quantity that has both magnitude and direction.

Velocity is the rate at which the position or displacement of a moving object changes. It is a vector quantity with both magnitude and direction. Mathematically, a velocity function $v(t)$ is the derivative of position function $x(t).$\vec v = \frac{d \vec x}{dt}$#### 6. Average Velocity The average velocity of a moving body is equal to its total displacement divided by the total time required to move a body from its initial position to its final position. Mathematically it is given by the equation$\bar{v} = \frac{x_2-x_1}{t_2 – t_1}$#### 3. Speed The rate at which an object moves along a path is defined as its speed. Speed is the magnitude of velocity, and it is always non-negative. Since it is a scalar quantity, it has no direction. #### 4. Average Speed The average speed of a moving object is determined by dividing the entire distance traveled by the total time it took to travel that distance. Average speed is the average rate of speed over the complete course of a trip. #### 7. Acceleration Acceleration is the rate of change of velocity. It is a vector quantity and has both magnitude and direction. Mathematically, acceleration function$a(t)$is a derivative of velocity function$v(t)$. It is first derivative of velocity function and second derivative of position function$x(t)$. It can be found by differentiating position with respect of time twice.$\vec a = \frac{d\vec v}{dt} = \frac{d^2 \vec x}{dt^2}\$

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