Instantaneous vs Average Velocity
Velocity is a very important concept discussed in mechanics. Many properties of an object such as the kinetic energy and viscosity depend on the velocity of the object. The concept of velocity is widely used in fields such as kinetics, kinematics, dynamics, astrophysics and even engineering. It is vital to have a proper understanding of the concepts of instantaneous velocity and average velocity in order to excel in such fields. In this article, we are going to discuss what instantaneous velocity and average velocity are, their similarities, the definitions of instantaneous velocity and average velocity and finally the difference between average velocity and instantaneous velocity.
What is Instantaneous Velocity?
One must understand the concept of velocity first, to understand the concept of instantaneous velocity properly. Velocity is a physical quantity of a body. The instantaneous velocity can be given as the instantaneous speed of the object with the direction the object is moving at that moment. In Newtonian mechanics, the velocity is defined as the rate of change of displacement. Both velocity and displacement are vectors. They have a quantitative value and a direction. The quantitative value alone of the velocity is called the modulus of velocity. This is equal to the speed of the object. The velocity of an object is directly related to the kinetic energy of the object. The theory of relativity suggests a more advanced version, which is not discussed here. The theory of relativity also suggests that the observed mass of an object increases when the velocity of the object is increased. The velocity of an object is dependent only on the changes of space-time coordinate of the object. The instantaneous velocity of the object is the distance the object has travelled in an infinitesimal time. This is mathematically denoted as dx/dt where x is the displacement vector. The instantaneous velocity can be considered as the velocity the object instantly feels. The instantaneous velocity is a function of time. For an object placed under a net force, the instantaneous velocity always changes. For an object moving with a constant velocity, the instantaneous velocity is a constant.
What is Average Velocity?
Average velocity is the average of the instantaneous velocities over a time- period. Since this is hard to obtain, an easy method is used to calculate the average velocity. The average velocity of a motion is the total distance travelled by the object divided by the time taken for the journey. If the path of the object is a straight line, a vector for the average velocity can be obtained easily. Another method for obtaining the average velocity is to integrate the instantaneous velocity with respect to time for the journey. This yields the distance travelled by the object. By dividing this quantity by the time taken for the journey, the average velocity can be calculated.
What is the difference between Average Velocity and Instantaneous Velocity?
• For a given journey, the instantaneous velocity is a function of time, but the average velocity is a constant.
• The vector of the average velocity is always on the direction of the displacement. Therefore, the average velocity is path independent, but the instantaneous velocity vector depends on the path taken.