Physics

# When is an object's average velocity equal to its instantaneous velocity?

If the velocity is constant (i.e., there is no acceleration). Terminal velocity is an example, although any constant velocity would fit this description.

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## Related Questions

For the instantaneous value of average velocity, average speed and average velocity are equal.

At a small time interval, the average velocity is approximately equal to the instantaneous velocity. However, the values of the average velocity and the instantaneous velocity approach each other , as the length of the time interval is decreased more and more.

Mainly, when the velocity doesn't change. Also, in the case of varying velocity, the instantaneous velocity might, for a brief instant, be equal to the average velocity.

When an object is in constant motion (when there is no acceleration). At any point in that motion the average and instantaneous velocities will be the same.

When there is no acceleration or when there is constant acceleration. When either of these cases is present, the graph of velocity versus time will be linear. When there is linear velocity, the average velocity will equal the instantaneous velocity at any point on the graph.

That is the case when you are talking about instantaneous speed and velocity - or when the velocity is constant. In the case of an average speed and velocity, this relation does not hold.

It equals an undefined entity. The average acceleration of an object equals the CHANGE in velocity divided by the time interval. The term "change in velocity" is not the same as the term "velocity", "average velocity", or "instantaneous velocity".

If the object begins from rest and a constant force is applied to it, then at the end of one second, the magnitude of its velocity is numerically equal to the magnitude of its average acceleration, although the units are different.

A distance-time graph shows the movement of an object with respect to time. The average slope between any two points on the graph is equal to the average velocity of the object between those two points. The instantaneous slope (or derivative) at a point on the graph is equal to the instantaneous velocity of the object at that point.

Yes. In smooth linear motion, the average speed and the instantaneous speed are equal.

Yes. For a start, this happens when the object moves at a constant velocity. Also, if moving in a straight line, even if the object changes speed there must needs be a moment when its instantaneous speed is equal to its average speed - since it cannot change speed suddenly, it must do so gradually.

Only if speed is constant. There can be no acceleration if the average speed is equal to the instantaneous speed.

The average acceleration of an object is equal to the instantaneous acceleration of that object if the acceleration is constant (i.e. linear when graphed). However, when there is not constant acceleration, there is no guarantee that the average acceleration is equal to the instantaneous acceleration (i.e. non-linear when graphed).

Never.Average velocity is total displacement (final position minus initial position) divided by the total time: vave = (xf-xi)/tAcceleration is the rate at which your velocity is changing or change in velocity over time: a= (vf-vi)/tThese two quantities may have the same numerical value but will never have the same units.Average velocity for a trip can equal instantaneous velocity at a certain point during the trip, however, at any time during a trip in which the velocity is constant or at half way through the total time of a trip where the acceleration is constant.

The magnitude of average velocity of an object equal to its average speed if that object is moving with CONSTANT velocity.

Because speed is the magnitude of the velocity vector. The velocity consists of the speed and the direction, and the whole thing can be embodied in a 3D vector. If you like the velocity is the magnitude (the speed), which is a scalar (just a real number), multiplied by a unit vector in the right direction.

Average acceleration will be equal to instantaneous acceleration when an object has an uniform acceleration throughout its motion. Example : A car accelerating at 1m/s2 uniformly in a straight line.

That's correct, the instantaneous magnitudes are equal. Non-instantaneous values may not be equal. For example, to find average speed, between two points, you divide the actual path distance by the time, but for average velocity you divide the straight line distance, between the points, by the time. The straight line distance could be quite a bit shorter then the actual path distance (for curved motion) so you could get a big difference between those averages. When calculating "instantaneous" values, however, the difference between "actual path distance" and "straight line distance" becomes insignificant, because you are using distances for infintesimally small time intervals.

Of course. When you're sailing along in the car on the highway with the "cruise control" on, and the ride is smooth as silk and the speedometer is pointing at ' 60 ' and never moving, your average and instantaneous speed are equal, until you do something to change your speed. And if the road is straight and you keep moving in a straight line, then the same statement is true of your velocity, as well as your speed.

Speed has only size. Velocity has size and direction.If three drivers are driving their cars at 50 mph headed north, 50 mph headed south, and50 mph headed east, their speeds are all equal, but their velocites are all different.Instantaneous speed is the speed at an instant in time. A point on the edge of an LP record hasthe same instantaneous speed whenever you look at it.Instantaneous velocity is the velocity ... speed and direction ... at an instant in time. A point on theedge of an LP record has a different instantaneous velocity every time you look at it. Even thoughthe speed is always the same, the direction keeps changing.

Acceleration is the derivative of velocity (a=dv/dt). If you are not familiar with calculus then it would be sufficient to say that the slope of the line tangent to the graph, only touches at one point, is equal to the instantaneous acceleration.

No, since momentum equals mass times velocity, if the masses of the two objects of equal velocity are different then their momentum will be different.

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