# Rectilinear Motion of Particles

Motion is one of the most common phenomenon we come across in our daily life. For example a moving car, a kid running on the road or a fly moving in the air all are said to be in motion. So in general terms a body is said to be in motion if it changes its position with respect to a reference point and time. Depending upon the path taken by the particle the motion can be of different types like projectile motion, rectilinear motion, rotational motion etc. For now we will only focus on rectilinear motion which is also known as linear motion.

When we require only one co-ordinate axis along with time to describe the motion of a particle it is said to be in linear motion. Some examples of linear motion are parade of soldiers, train moving along a straight line and many more.

## Distance and Displacement

So now that we have learnt about linear motion we will discuss about two terms related to change in position. These are called – ‘Distance’ and ‘Displacement’. Distance is defined as the total path length covered during a journey while displacement is the path length from final position of the particle to the origin O.

Consider the following figure:

We have an origin O, measurements to the right of O are taken as positive while to the left are taken as negative. Suppose a person starts from origin O reaches point A,

Distance = OA

Displacement = OA

Now he turns and reaches point B,

Distance = OA + AB

Displacement = -OB

As we can see displacement is negative since it is measured to the left of origin. From the above example we can infer that distance is always positive while displacement can either be positive or negative.

### Speed and Velocity

These terms are used to describe rate of change of position. Speed is the rate of change of distance while velocity is the rate of change of displacement. Comparing from above as distance can never be negative so speed is never negative while velocity can be both positive and negative. In mathematical terms, these are defined as follows:

Speed = $\frac{Distance~ Travelled}{Time ~Taken}$

Velocity =$\frac{(Final~ position – Initial~ position)}{Time~ Taken}$

So now we have basic ideas of rectilinear motion, to learn more about projectile motion, rotational motion come to BYJU’s classes.

#### Practise This Question

A spring of force constant 10 N/m has an initial stretch 0.20 m. In changing the stretch to 0.25 m, the increase in potential energy is about-