In physics motion of any object is an important and very general phenomenon. We many times have to deal with the motion of the objects. Various terms of the physics like velocity, time, distance, etc. are related and explained in various laws and equations of the motion. Sir Isaac Newton has given three laws of motion to describe the motion of massive bodies and how they interact. These laws and equations may seem obvious to us today, but more than three centuries ago they were considered revolutionary. In this article, the student will learn some important physics motion formula with suitable examples. Let us learn it!

**Table of content**

**Physics Motion Formula**

**What is the motion?**

Newton’s laws of motion are for the motion of massive bodies in a given inertial reference frame. This inertial frame of reference can be described as a 3-dimensional coordinate system that is either stationary or in uniform linear motion. These motions within such an inertial reference frame can be described easily by three simple laws.

These equations of motion relate the displacement of the moving object with its velocity, acceleration and time. The motion of a particle may follow many different paths. But in the here, we will focus on motion in a straight line, i.e. in a single dimension.

Since this motion is in one dimension, we will simply use signed magnitudes of the displacement, velocity, and acceleration. Also, negative values will be used to denote vectors in the opposite direction to positive quantities.

In simple words, if there is no acceleration, we will have the familiar formula:

s = v × t

Where,

s | displacement |

v | constant velocity |

t | time interval |

For a constant acceleration a, an initial speed u and an initial position of zero:

- Velocity:

v = \(v_0\) + at

- Displacement with positive acceleration

\((x – x_0) = v_0 t + \frac{1}{2} a \times t^2\)

- Displacement with negative acceleration

\((x – x_0) = v_0 t – \frac{1}{2} a \times t^2\)

- Velocity squared

\(v^2 = {v_0}^2 + 2a (x- x_0)\)

Where,

x | displacement |

\(x_0\) | constant velocity |

t | time interval |

v | velocity |

a | acceleration |

\(v_0\) | initial velocity |

**Solved Examples**

Q.1: A massive body slides along a frictionless surface with a constant acceleration of \(2 m s^{-2}\). At time t = 0 the block is at x = 5 m and traveling with a velocity of \(3 m s^{-1}\). Then determine,

a) Where is the block at t = 2 seconds?

b) What is the block’s velocity at 2 seconds?

Solution:

The given parameters are:

\(x_0\) = 5 m

\(v_0 = 3 m s^{-1}\)

\(a = 2 m s^{-2}\)

(a) Formula is

\((x – x_0) = v_0 t + \frac{1}{2} a \times t^2\)

Substitute t = 2 seconds and the appropriate values of \(x_0 and v_0\).

\(x = 5 + 3 \times 3 + \frac{1}{2} \times 2 \times 2^2\)

= 5 m + 6 m + 4 m

= 15 m

The body will be at the 15 meter mark at t = 2 seconds.

(b) This time, Equation 2 is the useful equation.

v = v_0 + at

= 3 + 2 × 2

= \(5 m s^{-1}\)

The body will be travelling \(7 m s^{-1}\) at t = 2 seconds.