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Velocity is the first derivative of position (I'll denote X) with respect to time, t. It is usually written V = dX/dt, or f'(t), whichever notation is more convenient. For example, if an object's position in free-fall (in meters) is given by X = -4.9t2 + 10t + 200, then dX/dt = -9.8t + 10 (applying the power rule), and dX/dt evaluated at, say, t = 4 s, is equal to -9.8(4) + 10 = -29.2 m/s (hence, 29.2 m/s downward).
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What is the relationship between average velocity and instantaneous velocity?
The average velocity over an time interval is the average of the instantaneous velocities for all instants over that period. Conversely, as the time interval is reduced, the average velocity comes closer and closer to the instantaneous velocity.
Can the average velocity of the body be the same as instantaneous velocity?
Yes, the average velocity of the body can be same as the instantaneous velocity at a small time interval.The values of the average and the instantaneous velocities approach each other , as the length of time interval is decreased.
When an object moves with inconstant velocity does its average velocity differ from its instantaneous velocity?
Generally it is a Yes. Instantaneous velocity is the exact velocity at a particular time in the course of the movement. However, average velocity is the average of all the instantaneous velocity over a period of time. It is also known as speed in everyday life. As a result, the movement of an object over a time period under varying velocity denotes a varying instantaneous velocity which could be different from the average velocity. It is however, possible that the instantaneous velocity equates to the average velocity at a certain point over the duration of movement. For example, a ball is traveling at instantaneous velocity of 99m/s at t=1s , 100m/s at t=2s and 101m/s at t=3s. the average velocity over the 3s period is hence 100m/s which coincides with the instantaneous speed at t=2s.
When Velocity of particle equals average velocity equals instantaneous equals speed is possible?
When the length of the time is decreased more and more ,average velocity of the particles equals instantaneous velocity.
What is the formula of velocity?
There are several definitions. not just one. Average velocity in a direction = Average displacement (distance) in that direction/time Instantaneous velocity in a direction = derivative of displacement in that direction with respect to time Average velocity in a direction = Initial velocity in that direction + Average acceleration in that direction * time Instantaneous velocity in a direction = Definite integral of acceleration in that direction with respect to time, with initial velocity at t = 0 Then there are others in which time is eliminated.
