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When the velocity is constant, can the average velocity over any time interval differ from the instantaneous velocity at any instant? If so, give an example; if not, explain why.

When the velocity is constant, can the average velocity over any time interval differ from the instantaneous velocity at any instant? If so, give an example; if not, explain why.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
For constant velocity, the average velocity of a particle between any time interval will be the same as the instantaneous velocity at any instant.
It is important to note that the velocity will be constant, if the particle moves in straight line and takes no curves. Therefore the position versus time graph for the particle will be a straight line. Hence, the slope of the position time graph, representing the instantaneous velocity of the particle will always be constant.
Consider for example, the motion of the car along a straight road, such that the car moves with constant velocity i.e. the car travel equal displacement in some fixed time interval. As the car takes no turn, its velocity vector always point in the same direction and the length of the vector also remains the same.
The instantaneous velocity of the car at any instant is the slope of the position time curve at a particular point. As stated above, the position time curve for the car is a straight line. Therefore its slope at any point will be same and equal to the average velocity.

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