= m s – and at t = . s, v = m s - . . .
. . Average velocity – . .
b b b × - . . = m s × Note that for uniform motion, velocity is the same as the average velocity at all instants . Instantaneous speed or simply speed is the magnitude of velocity.
For example, a velocity of + . m s – and a velocity of – . m s – — both have an associated speed of . m s - .
It should be noted that though average speed over a finite interval of time is greater or equal to the magnitude of the average velocity, instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant. Why so ? . ACCELERATION The velocity of an object, in general, changes during its course of motion.
How to describe this change? Should it be described as the rate of change in velocity with distance or with time ? This was a problem even in Galileo’s time. It was first thought that this change could be described by the rate of change of velocity with distance.
But, through his studies of motion of freely falling objects and motion of objects on an inclined plane, Galileo concluded that the rate of change of velocity with time is a constant of motion for all objects in free fall. On the other hand, the change in velocity with distance is not constant – it decreases with the increasing distance of fall. This led to the concept of acceleration as the rate of change of velocity with time. The average acceleration a over a time interval is defined as the change of velocity divided by the time interval : = ∆ ( .
) where v and v are the instantaneous velocities or simply velocities at time t and t . It is the average change of velocity per unit time. The SI unit of acceleration is m s – .