Differences between acceleration and velocity

To study 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 the motion of an object, which is also said as displacement.

The motion of an object

Consider an object 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.

Different types of 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

Scalar 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.

Vector quantities

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.

Units

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 are called 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/s2 or ms–2 or Newton, abbreviated as N. Here “m” is the abbreviation of metre of the physical quantity length and “s” is the abbreviation of the second of the physical quantity time. Another example of a derived quantity is density. It is expressed as kg/m3 or kgm–3. Here, “kg” is the abbreviation of kilogram of physical quantity mass and “m” is the abbreviation of metre of the physical quantity length.

The displacement of an object is defined as the vector difference between the starting point to the ending point of a displaced object. 

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

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

Definition of velocity

The rate of change of displacement is velocity. When an object is moving in a specific direction with respect to time, it 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 the 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

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

The common use of the word “acceleration” refers to 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 rate of change of velocity is 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 dropped into the water. When the pebble is dropped, its initial speed is zero, when it hits the water, its speed increases due to the 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/s2 or ms–2.

Difference between Velocity and Acceleration

These are the differences between velocity and acceleration.