**Rectilinear Motion** (or **Linear Motion**) is a specific form of motion. It is a motion that occurs in a single direction or axis. All the motion-related parameters are along one direction. Hence, the motion is also called motion in one dimension**. **

Index

## Rectilinear Motion Definition

Rectilinear motion definition can be stated as a *motion that occurs along a *** single direction only**. It can also be called straight-line motion. The entire motion can be described without needing to use vectors.

## Rectilinear Motion Examples

Here are some of the rectilinear motion examples from our daily life.

- An athlete running on a track
- A bead moving on a fixed rod
- A train moving on a straight track
- Swimmer swimming in parallel
- An object falling straight down

## Quantities Involved

Here we discuss some quantities involved in linear motion.

### Distance

It is the** total distance** covered by the moving object/particle. For example, if an object moves 10 meters forward and 6 meters backwards, the total distance covered is **10+6 = 16 meters**.

### Displacement

It is the **NET distance** between starting and endpoint of motion. Using the same example as above, if the body moves 10 m forwards and 6 m backwards, it is only (10-6) m away from starting point. Thus, displacement is just 4 meters**.**

### Velocity

**Velocity** \((\mathbf{v})\) is the rate of change of displacement. It has a direction. In linear motion, this direction is represented by a positive or negative sign. The **boldface** indicates the fact that it has a direction.

**Average Velocity**

It is given by the displacement \(\mathbf{s_2 – s_1}\) divided by the total interval of time \((t_2 – t_1)\) it takes cover.

In other words,

\(\bar{\mathbf{v}} = \frac{\mathbf{s_2-s_1}}{t_2 – t_1}\)

**Instantaneous Velocity**

It is the **limit of average velocity** when *time interval goes to zero*. It gives the velocity of an object at a specific instant.

\(\mathbf{v} = \lim_{{(t_2 – t_1)} \rightarrow 0} \frac{\mathbf{s_2-s_1}}{t_2-t_1} = \lim_{{\Delta t} \rightarrow 0} \frac{\mathbf{\Delta s}}{\Delta t} = \frac{d\mathbf{s}}{dt}\)

Thus, it is the time-derivative of displacement.

### Speed

Speed (\(v)\) is the magnitude of velocity. As such, it has no direction and is always non-negative. Unlike velocity, it is denoted without boldface as it has no direction.

**Average Speed**

It is denoted by \(\bar{v}\). It can be given by distance (\(Delta d)\) covered in a given time interval \((\Delta t)\).

Mathematically,

\(\bar{v} = \frac{\Delta d}{\Delta t}\)

### Acceleration

It is the **rate of change of velocity**. It is denoted by \(\mathbf{a}\). The *boldface denotes that it has direction*. In linear motion, the direction is given by the sign.

Mathematically,

\(\mathbf{a} = \frac{d\mathbf{v}}{dt} = \frac{d^2 \mathbf{s}}{dt^2}\)

## Types of Rectilinear Motion

Now, let us discuss different types of rectilinear motion we encounter on daily basis.

### Uniform Rectilinear Motion

In this type of linear motion, **velocity is constant**. There is *no acceleration* and *no net external force* acting on the object.

### Uniformly Accelerated Rectilinear Motion

In this linear motion, **velocity is changing** but the **acceleration is constant** also known as *Kinematic Equations*. The motion of the body an be given by the three equations of motion

\(\mathbf{v} = \mathbf{u} + \mathbf{a}t\)

\(\mathbf{s} = \mathbf{u}t + \frac{1}{2} \mathbf{a} t^2\)

\(\mathbf{v^2} – \mathbf{u^2} = 2 \mathbf{a} \cdot \mathbf{s}\)

**Know more on Rectilinear Motion Formula**

### Non-uniformly Accelerated Rectilinear Motion

Here, *neither velocity nor acceleration is constant*. Both can vary with time.

## FAQs

**What is rectilinear motion?**It is a type of motion that happens along one direction or axis only. It is also known as linear motion.

**What is the difference between velocity and speed?**Velocity is the rate of change of displacement, it has both *magnitude and direction*, while speed is simply the magnitude of velocity, it *doesn’t have direction.*

**What are the three equations of motion?**The **three equations of motion** are:

\(\mathbf{v} = \mathbf{u} + \mathbf{a}t\)

\(\mathbf{s} = \mathbf{u}t + \frac{1}{2} \mathbf{a} t^2\)

\(v^2 – u^2 = 2 \mathbf{a} \cdot \mathbf{s}\)

They are applicable for **uniformly accelerated motion.**

**What is the difference between rectilinear and curvilinear motion?****Rectilinear motion** occurs in a* single direction*, and is thus one-dimensional. It can be called motion in a straight line.**Curvilinear motion** occurs *along a curve *rather than a line. It can thus be two- or three-dimensional.