Distance and displacement are two terms which measures the same quantity, length but in different ways. Distance is the total length covered by a moving body while displacement is the possible shortest distance covered by the body. Both quantities are measured in unit of length, meter(m).

**Distance**

It is the actual length of path covered by body. From speed formula we have,

Speed = Distance / Time

Or, **Distance = Speed x Time**

**Displacement**

It is the shortest path covered by the body which can be calculated by differencing initial and final distance value.

Numerically,

Displacement = u – v

Where, u = initial distance & v = final distance.

Also, from velocity formula,

Velocity = Displacement / Time

Or, **Displacement = Velocity x Time**

Distance is always greater or equals to displacement.

i.e Distance ≥ Displacement

or, **Distance / Displacement ≥ 1**

## Difference Between Distance and Displacement

Distance | Displacement |
---|---|

It is the actual path covered by a body. | It is the shortest distance between initial and final point by a moving body. |

It is scalar quantity. | It is vector quantity. |

Formula = speed x time | Formula = velocity x time |

Denoted by ‘d’ without any arrow on its head. | It is denoted by ‘s’ with arrow on its head. |

Distance covered by a moving body cannot be zero. | Displacement covered by body may be zero. Ex, body moving in a circle. |

Its value is never negative. | Its value may be negative. |

With respect to time, distance always increases. | With respect to time, displacement may increase or decrease. |

It gives the detailed route followed by the moving body. | It only provides the initial and final locations in the route. |

Distance is always greater or equals to displacement. | Displacement is less or equal to distance. |

From distance and time value, we can find speed of moving body. | From displacement and time value, we can find velocity of moving body. |

## Numerical based on distance and displacement

**Numerical 1**

Calculate the value of distance and displacement from following figure.

Distance = 5 + 3 + 5 + 3 = 16m (sum of all distance covered)

Displacement = 3m (shortest possible distance)

**Problem 2**

On seeing a deer, a lion runs at speed of 40meter/min and catches the deer in 30 minutes. Calculate the distance travelled by lion to catch the prey.

__Solution__

We have__,__

Speed = 40m/min

Time = 30min

From distance formula,

Distance = speed x time

= 40m/min x 30min

= 1200 meter

**Problem 3**

Calculate the distance and displacement covered by a body moving in a circle.

__Solution__

From the circle,

Distance is equal to the circumference of the circle.

So, Distance = 2πr

And, displacement is zero since the man return to its initial position

Displacement = 0

Hence distance is equal to 2πr and displacement is equal to 0 for the body moving in a circle.

__Problem 4__

Calculate the distance and displacement covered by body on completing half circle.

__Solution__

From the semi-circle

Distance is equal to half of the circumference of the circle.

So, Distance= πr

And displacement is equal to the diameter or 2 times the radius of the circle

i.e Displacement = 2r

Hence distance is equal to πr and displacement is equal to 2r for the body moving in semi-circle.