# Kinematic Equations Made Easy

I don’t feel that I should explain the importance of kinematics in Physics. **Kinematic equations** form the very foundation of any question you intend to solve in physics. Be it uniform rectilinear motion or rotational motion, these equations will always help you to find the correct answer.

Whether you are preparing for NEET or JEE you must have a strong command in kinematics if you want to crack these types of competitive exams. Here in this article, I have tried to strengthen your concepts by explaining all types of kinematic equations.

## What are Kinematic Equations?

Kinematic equations are equations showing the dependence of the main kinematic characteristics (radius vector, coordinates, velocity, acceleration) on time.

## Basics of Kinematics

In mechanics, we will use five basic SI units:

Measurement | Unit | Symbol |
---|---|---|

Mass | Kilogram | kg |

Length | Meter | m |

Time | Second | s |

Angle | Radian | rad |

Solid Angle | Steradian | cf |

The quantities used in physics are of two types:

**Scalar Quantity**— A scalar is a value characterized by a numerical value (it can be positive or negative).**Example:**Speed**Vector Quantity**— A vector is a quantity characterized by both a numerical value (modulus of a vector, a positive number) and a direction.**Example:**Velocity

There are five **Kinematic Variables** that link any type of kinematic equation. They are:

Displacement | Δx |

Initial velocity | v or _{0}u |

Final velocity | v or v_{f} |

Time interval | t |

Constant acceleration | a |

## Kinematic Equations

These can be grouped into Rectilinear Kinematics equations for linear motion and Rotational Kinematics Equations for angular motion. Let’s have a look:

### Basic Kinematic Equations for Linear Motion

The translational or linear motion of the body is the one in which all its points move along the same trajectories and at any given moment they have equal speeds and equal accelerations. There are four basic equations of kinematics for linear or translational motion. These are:

$$v=v_0+at$$

$$Δx=t(v+v_0)/2$$

$$Δx=v_0t+\frac{1}{2}at^2$$

$$v^2=v_0^2+2 a Δx$$

Additional point: If you are asked to find displacement is nth second then use this formula-

$Δx=u+1/2a(2n-1)$ where n is the nth duration of time.

Questions are frequently asked based on this formula. Do use it and thank me later!

**Remember: These equations are only applicable when there is uniform motion, and acceleration and velocity, both are constant.**

Let me give you one example:

Suppose a car is moving with an initial velocity of 20m/s and comes to rest in 5 seconds. You are asked to find acceleration and displacement covered.

**Solution:** According to the question the initial velocity , u =20m/s

Since the body is coming to rest that means the final velocity, v= 0 m/s

Time taken by the body to come to rest, t=5 sec

So, applying the first equation of motion we get, v= u +at, i.e 0=20 + 5a

thus, acceleration, **a = $-4m/s^2$**

Now, since the body is coming to rest after time, t that means there is some retarding force that is being applies to the body to to which is comes to rest , since the acceleration is negative that means the retardation is occuring against the direction of motion.

Now, to find the **displacement** we can use second equation , so

$Δx=t(v+v_0)/2$

thus, Δx= 5(20+0)/2 = 50m.

**Also read:** Tunnel Through the Earth

### Rotational Kinematics Equation for Angular Motions

Rotational motion is a movement in which all points of the body move in circles, and the centers of all the points lie on one straight line – the axis of rotation. There are few changes when compared to linear equations of motion.

- Displacement is replaced by a change in angle and it is denoted by theta (Θ)
- Velocities are replaced with angular velocities
- Acceleration is replaced by angular acceleration
- Time remains constant

$$ω=ω_0+αt$$

$$Θ=1/2(ω+ω_0)t$$

$$Θ=ω_0t+1/2αt^2$$

$$ω^2=ω^2_0+2αΘ$$

where ω is the final angular velocity, $ω_0$ is the initial angular velocity, t is time and Θ is displacement and α is angular acceleration.

*Conclusion*

This was all about **kinematic equations for both linear and angular motions.** I hope I was able to make your concepts a bit clearer so that you don’t face any problems while solving questions on mechanics. Do utilize the concepts and prepare well. *Happy learning!*

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