To study on velocity, acceleration and the differences between them, first a detailed study about the concept of motion is necessary. Not only that but also other basic definitions like scalar and vector quantities, expressing units and so on should be known. First, let us see on motion of an object, which is also said as displacement.

**The m****otion of an object**

**Different types of Motion**

*Scalar quantities*

*Vector quantities*

*Units*

**Definition of Displacement**

**The displacement of an object is defined as the vector difference between ****the ****starting ****point**** to ****the ****ending point of a displaced object**. **The rate of change of displacement is velocity**. When an object is moving in a specific direction with respect to time is said to be velocity, i.e., the quantity that specifies both distance and time is called velocity. The velocity of an object can be changed by changing the speed, direction or both of that object.

In other words, it is defined as the displacement produced per unit time.

Velocity = Displacement / Time

=*x* / *t*

Where*x* is the distance travelled in a given direction, i.e., displacement. It is calculated as the difference between the positions.

*x* = Final point – Initial point

=*v* – *u*

*t*, time taken to travel the distance.

*V =** d** / t*

Velocity*V* is calculated as the change in displacement with respect to time. It is a vector quantity as it is dependent on both magnitude and direction.

For example, travelling in a car at a speed of 20 m/s towards the north in 2 minutes; this explains that the car moved with what speed, in what direction and time took for this displacement.

Hence, velocity is a vector quantity. Vector quantity involves not just the magnitude but also the direction, i.e., two-dimensional. SI unit of velocity is m/s or ms^{–1}.

**Definition of Speed**

Consider an object is moving from a fixed known point (as well as its position) with respect to its external influence, then the object is said to have undergone a motion.

There are four types of motion. They are rotary, oscillatory, reciprocate and linear. In all these types, the motion is set to happen with respect to time. Though the motion variation is slight, they all have a different notion. For example, for rotational motion, the displacement is called angular displacement and likewise for velocity, angular velocity and so on.

**Scalar and Vector quantities**

A scalar quantity is the measure of a quantity which is one-dimensional, i.e., only its magnitude; for example, temperature, work, mass and so on.

A vector quantity is the measure of a quantity which is two-dimensional, i.e., both its magnitude and direction; for example, displacement, velocity, acceleration and so on.

A unit of measurement is the definite magnitude of a quantity. All measurements and their expression of the units are followed based on the International System of Units. There are seven basic units. They are as follows:

Other sets of quantities are there, which is called as derived quantities. They are a combination of seven basic units. Simply, they are derived from the fundamental quantities. Say, for example, the unit of force is m/s^{2} or ms^{–2} or Newton, abbreviated as N. Here “m” is the abbreviation of **meter** of the physical quantity **length** and “s” is the abbreviation of **second** of the physical quantity **time**. Another example of a derived quantity is **density**. It is expressed as kg/m^{3} or kgm^{–3}. Here “kg” is the abbreviation of **kilogram** of physical quantity **mass** and “m” is the abbreviation of **meter** of the physical quantity **length**.

S.No. | Physical Quantities | SI Units |

1 | Length | meter (m) |

2 | Mass | kilogram (kg) |

3 | Time | second (s) |

4 | Electric current | ampere (A) |

5 | Temperature | kelvin (K) |

6 | Luminous intensity | candela (cd) |

7 | Amount of substance | mole (mol) |

Other sets of quantities are there, which is called as derived quantities. They are a combination of seven basic units. Simply, they are derived from the fundamental quantities. Say, for example, the unit of force is m/s

Consider a body is moving from its rest position O. It travels a distance of *x* and stops at a point P. The distance between point O and point P is measured as *x*. Thus, the change of position of a body is known as displacement.

Displacement is not to be necessarily the same as distance travelled every time.

Displacement*d* = P – O = *x** *m (m, unit of length)

**Definition of Velocity**

Displacement

In other words, it is defined as the displacement produced per unit time.

Velocity = Displacement / Time

=

Where

=

Velocity

For example, travelling in a car at a speed of 20 m/s towards the north in 2 minutes; this explains that the car moved with what speed, in what direction and time took for this displacement.

Hence, velocity is a vector quantity. Vector quantity involves not just the magnitude but also the direction, i.e., two-dimensional. SI unit of velocity is m/s or ms

Speed is the distance travelled by an object in a given time. Speed is a scalar quantity as it expresses only the magnitude and not the direction.

Speed = Distance / Time

Velocity and speed are similar with respect to the motion of an object. In simple words, velocity is the speed with direction. Velocity includes direction with displacement whereas speed includes only distance travelled.

**Definition of ****Acceleration**

Speed = Distance / Time

Velocity and speed are similar with respect to the motion of an object. In simple words, velocity is the speed with direction. Velocity includes direction with displacement whereas speed includes only distance travelled.

The common use of the word “acceleration” gives about moving or increasing with high speed. But the actual meaning is the change of speed, i.e., change of velocity (by increasing or decreasing the speed). **The rat****e of change of velocity is acceler****ation**.

As we have seen before, velocity is said to be the speed with direction. In other words, when there is a change in velocity, consequently the acceleration exists.

For example, consider a pebble is dropped into the water. When the pebble is dropped, its initial speed is zero, when it hits the water its speed increases due to earth’s gravity. So the water splashes up. Therefore acceleration is defined as the rate of change of velocity. If the velocity of a body is changed from “u” to “v” in time “t”, then acceleration is given as follows.

Acceleration = Change in velocity / Time taken

= Final velocity – Initial velocity/time taken

*A = **d(**u–v**) / **dt*

As it has both magnitude and direction, it is a vector quantity. SI unit of acceleration is m/s^{2} or ms^{–}^{2}.

**Difference between Velocity and Acceleration**

These are the differences between velocity and acceleration.

As we have seen before, velocity is said to be the speed with direction. In other words, when there is a change in velocity, consequently the acceleration exists.

For example, consider a pebble is dropped into the water. When the pebble is dropped, its initial speed is zero, when it hits the water its speed increases due to earth’s gravity. So the water splashes up. Therefore acceleration is defined as the rate of change of velocity. If the velocity of a body is changed from “u” to “v” in time “t”, then acceleration is given as follows.

Acceleration = Change in velocity / Time taken

= Final velocity – Initial velocity/time taken

As it has both magnitude and direction, it is a vector quantity. SI unit of acceleration is m/s

Velocity | Acceleration |

Velocity is the rate of change of displacement. | Acceleration is the rate of change of velocity. |

Velocity is a vector quantity because it consists of both magnitude and direction. | Acceleration is also a vector quantity as it is just the rate of change of velocity. As velocity is a vector quantity, obviously, acceleration is also. |

Velocity may be positive or negative or zero. | Acceleration may be positive or negative. It cannot be zero as it is defined as the change in velocity or speed. This explains that there should be some motion for acceleration. |

SI unit is m/s or ms^{–1}. | SI unit is m/s^{2} or ms^{–2}. |

Formula for velocity = displacement / time | Formula for acceleration = velocity / time |

These are the differences between velocity and acceleration.