Kinematic Equations - II

The first kinematic equation expresses velocity as a function of the initial velocity and the change in velocity.

For deriving the second kinematic equation, two equations for average x velocity are used during an interval from t equal to zero to a later time t. The first equation for average x velocity is the change in displacement over the change in time, as discussed in previous lessons. Here, the initial position is denoted by x₀ at time t equal to zero and x at later time t.

Assuming acceleration to be constant, the average x velocity can also be represented as the average of the velocities at the initial and final times. Substituting the first kinematic equation here, an equation for the position x as a function of time is obtained.

This equation shows that the position of an object at any time t is the sum of its initial position, the distance moved under constant initial velocity, and the distance traveled during the change in velocity.