Acceleration

All bodies have intrinsic property to maintain its velocity. This is a fundamental nature of matter. However, a change in the velocity results when a net external force is applied. In that situation, velocity is not constant and is a function of time.

In our daily life, we are often subjected to the change in velocity. The incidence of the change in velocity is so common that we subconsciously treat constant velocity more as a theoretical consideration. We drive car with varying velocity, while negotiating traffic and curves. We take a ride on the train, which starts from rest and comes to rest. We use lift to ascend and descend floors at varying speeds. All these daily life routines involve change in the velocity. The spontaneous natural phenomena are also largely subjected to force and change in velocity. A flying kite changes its velocity in response to wind force as shown in the figure below.

The presence of external force is a common feature of our life and not an exception. Our existence on earth, as a matter of fact, is under the moderation of force due to gravity and friction. It is worth while here to point out that the interaction of external force with bodies is not limited to the earth, but extends to all bodies like stars, planets and other mass aggregation.

For example, we may consider the motion of Earth around Sun that takes one year. For illustration purpose, let us approximate the path of motion of the earth as circle. Now, the natural tendency of the earth is to move linearly along the straight line in accordance with the Newton’s first law of motion. But, the earth is made to change its direction continuously by the force of gravitation (shown with red arrow in the figure) that operates between the Earth and the Sun. The change in velocity in this simplified illustration is limited to the change in the direction of the velocity (shown in with blue arrow).

This example points to an interesting aspect of the change in velocity under the action of an external force. The change in velocity need not be a change in the magnitude of velocity alone, but may involve change of magnitude or direction or both. Also, the change in velocity (effect) essentially indicates the presence of a net external force (cause).

Acceleration

Acceleration

Acceleration is the rate of change of velocity with respect to time.

It is evident from the definition that acceleration is a vector quantity having both magnitude and direction, being a ratio involving velocity vector and scalar time. Mathematically,