## Speed and velocity

Speed and velocity is not same in Physics. Let us learn speed and velocity here.

### What is speed?

The rate of change of distance with respect to time is called as speed of a body.

### Properties of speed heaving bodies

1) The speed of a particle or a body defined as the distance traveled by it in a unit of time i.e speed= distance/time.

2) Speed is a scalar quantity.

3) The speed of a body can be increase or decrease with time.

4) The cgs unit of speed is cm/s and S.I. unit is m/s.

5) The dimensional formula of speed is [M^{0}L^{1}T^{-1}].

6) If the speed of a body is zero, the body is at rest.

7) The distance time graph of a body at rest, is a st. line parallel to time axis.

### Uniform speed

i) A body is said to be moving with a uniform speed, if it covers equal distance is equal intervals of time, however small these intervals may be.

ii) When a body moves with a constant speed, distance travelled by it in each second is the same. The distance travelled at the end of 1st, 2nd,3rd, …second will be in the ratio 1:2:3… .

### Variable speed

A body is said to be moving with a variable speed if it covers equal distance in unequal intervals of time or unequal distance in equal intervals of time, howsoever small these intervals may be.

### Average or Mean speed

When a body is moving with a variable speed, then the average speed of the body is defined as the ratio of total time taken i.e. Average speed = Total distance travelled/Total time taken.

### Instantaneous speed

i) When a body is moving with a variable speed, then the speed of the body at given instant of time is called its instantaneous speed.

ii) In case of a uniform motion, the instantaneous speed of body is equal to its uniform speed.

iii) The speedometer in an auto vehicle measures its instantaneous speed.

### What is velocity?

The rate of change of displacement with respect to time is called as velocity.

### Properties of velocity heaving bodies

1) The velocity of a particle or a body is defined as the time rate of change of displacement of it.

2) Velocity of a particle is defined as the distance covered by a particle in a particular direction with respect to the point of reference.

3) The velocity of a body is a vector quantity.

4) The velocity of a body can be 0, negative or positive.

5) Velocity of a body can be equal to speed only if the body is moving along a st. line in the same direction.

6) The velocity of a body can never be greater than the speed of the body.

7) CGS unit of velocity is cm/s and S.I. unit is m/s.

8) Dimensional formula of velocity is [ M^{0}L^{1}T^{-1}].

9) If the velocity of a body is 0, then the body is at rest.

#### Uniform velocity

i) A body is said to be moving with a uniform velocity, if it undergoes equal displacement in equal displacement in equal intervals of time, howsoever small these intervals may be.

ii) When a body is said to be moving with a uniform velocity, it is moving along a st. line and its motion is called uniform motion in one dimension.

iii) Velocity-time graph of a uniform motion is a st. line parallel to time axis.

iv) The Velocity-time graph of a uniform motion is a st. line inclined to time axis.

#### Variable velocity

A body is said to be moving with a variable velocity, if it undergoes equal displacement in equal displacement in unequal intervals of time or unequal displacement in equal intervals of time or changes direction of motion while moving with a constant speed.

#### Average or Mean velocity

i) When a body is said to be moving with a variable velocity, then the average velocity of the body for a given time is defined as the ratio of the total displacement of the body to the total time taken i.e. Average velocity = total displacement/total time taken.

ii) When a body is moving with a uniform velocity, its average velocity is equal to its uniform velocity.

#### Instantaneous velocity

i) When a body is moving with a variable velocity, then the velocity of the body at a given instant of time is called its instantaneous velocity.

ii) In case of uniform motion, the instantaneous velocity of a body is equal to its uniform velocity and also equals to the average velocity of the body.