Formulas to Calculate Motion Along a Straight Line

When an object travels in a straight line and covers the same distance, and the velocity varies by different amounts, it is said that the object is in non-uniform motion. In other words, the rate of change in velocity is different at different time intervals.

E.g., Consider the example of a kid playing with balls. He throws the first call at a distance of 6 m. In the successive two attempts, the ball is thrown at a distance of 10 m both times. In all cases, the velocity is differently applied by the boy. 

Motion 

The change in the position of an object with regard to the time taken is called motion. In simple words, if a body is moving, it is described as motion. The motion might be slow or swift, but it will exist in every moving body. Motion can be described in terms of time, speed, displacement, and distance. 

For example, let’s assume an object moves from Point A to Point B and changes its position with a change in time. Here, we can see that the object is undergoing motion. 

In our day-to-day life, we see numerous objects moving around us. Here are a few examples of objects in motion.

• The water flowing out of the tap
• People walking on the streets
• Vehicles running on the roads
• Birds flying in the air
• The pen falling from the table
• A fruit falling from a tree

Types of Motion

We all have observed various objects move in different ways. Some objects move along a straight path, some exhibit a curved motion, and so on. Motion is categorised into three types according to the nature of the object’s movement:

• Rotary Motion
• Motion in Straight Line or Linear Motion
• Oscillatory Motion

Motion in Straight Line

Motion in a straight line is the movement of an object in a straight line. It is also known as the rectilinear motion. However, it is different from generic motion. Linear motion, as previously stated, is a one-dimensional motion. The motion of an object has both magnitude and direction, i.e. the position and velocity of an item are given as vector values.

Based on the nature of displacement, linear motion is classified into:

1. Uniform motion
2. Non-uniform motion

Uniform Motion in the Straight Line

When an object travels in a straight line and covers the same distance in the same time, it is said that the object is in uniform motion. Simply, the rate of change in velocity will always remain constant in the case of uniform acceleration. 

Non-uniform Motion in a Straight Line

When an object travels in a straight line and covers the same distance; however, the velocity varies by different amounts, then it is said that the object is in non-uniform motion. In other words, the rate of change in velocity is different at different time intervals.

For eg:- Consider the example of a kid playing with balls. He throws the first call at a distance of 6 m. In the next two attempts, the ball is thrown at a distance of 10 m both times. In all cases, the velocity is differently applied by the boy.

A List of All Formulas to Calculate Motion in Straight Line

Here is the list of all the formulas which can be used in calculating Motion in a Straight Line:

1. Average Speed 

• Average Speed is the ratio of total path length covered in a given interval of time.
• Mathematically, 

Average speed = Total distance covered/Total time taken

                                                       vav=xt

1. Average velocity 

• Average velocity is the displacement of an object over time. It is the displacement per unit time. Let x1 and x2 be positions of an object at times t1 and t2, respectively.
• Mathematically, 

Average velocity= displacement time = x2 – x1t2 – t1  

1. Acceleration

• Sometimes the speed of an object, while travelling in a car or bus, becomes fast or slow, indicating a change in velocity with respect to time. Acceleration is the rate of change of velocity with respect to time. Acceleration is a vector quantity. SI unit of acceleration is ms-2.
• Mathematically, 

vav = xt ………equation (2)

     aav= v2–v1t2–t1=vt

1. Relative velocity

• The relative velocity of an observer A in the rest frame of another observer B is the velocity of the observer A in the frame of reference of observer B. The following is the general formula for velocity:
• vA – vB is the velocity of observer A in relation to observer B. The concept of relative velocity is described by this simple formula.

                                                            vAB  = vA – vB

1. Equations of motion in a straight line

1. v=u+at
2. s=ut+½ at2

iii. v2=u2+2as

where

v= final velocity

u=initial velocity

s= displacement

a=acceleration

t=time

Conclusion

In this article, we have gone through motion in a straight line and covered various types of motions, their formulas, and examples. We have read that the change in the position of an object with respect to time is called motion. In simple words, if a body is moving, it is described as motion. The motion might be slow or swift, but it will exist in every moving body. Motion can be described in terms of time, speed, displacement, and distance.

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