Physics

# Does the instantaneous speed ever equal the magnitude of its average velocity?

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###### 2013-12-18 16:51:31

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.

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## Related Questions

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.

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.

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.

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

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.

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

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".

1. magnitude of distance covered is equal to the magnitude of displacement. 2. the motion of the object is in a straight line i.e. in a particular direction.

Instantaneous velocity mean change of displacement in extremely small amount time. (in math way, taking[ lim t---&gt;0 (change in displacements/change in time) ]. instantaneous speed is the same expect displacement change to distance. So,because of very very small change in time, magnitude of distance and displacement will be same for any direction the object is moving.

The magnitude of the velocity is always equal to the speed. But velocity is a vector quantity (has a magnitude and direction) while speed is just a scalar quantity (only magnitude). So velocity and speed are never equal.

-- The magnitude of acceleration is equal to the time rate of change of speed. -- The magnitude of acceleration is equal to the time rate of change of the magnitude of velocity. -- Acceleration and velocity are both vectors.

Yes usually and no rarely, velocity is defined as a vector, having both a direction and a magnitude (which is speed in the case of velocity). For instance 100 mph (speed) east (0o) (direction). In this form it is easy to see that the magnitude is 100 mph but mathematically to determine the magnitude of a vector you would divide the vector by its direction. 100 mph 0o / 0o = 100 mph Average speed and average velocity share the same relationship as instantaneous speed and instantaneous velocity so divide out the average direction from your average velocity to determine your average speed. If this is over a time period and you know the beginning and ending places in space your averages will simply be the difference from the starting to the ending places. So yes so long as you define speed to actually be the magnitude of the vector. However, if speed is taken without direction over time it may become something different. If an object travels along a vector with a negative magnitude its speed will not be negative but its vector magnitude will. Ex: A car travelling in reverse still has a positive speed but a compass will show it to be heading in the opposite direction of travel, a negative vector value...

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 usually and no rarely, velocity is defined as a vector, having both a direction and a magnitude (which is speed in the case of velocity). For instance 100 mph (speed) east (0o) (direction). In this form it is easy to see that the magnitude is 100 mph but mathematically to determine the magnitude of a vector you would divide the vector by its direction. 100 mph 0o / 0o = 100 mph Average speed and average velocity share the same relationship as instantaneous speed and instantaneous velocity so divide out the average direction from your average velocity to determine your average speed. If this is over a time period and you know the beginning and ending places in space your averages will simply be the difference from the starting to the ending places. So yes so long as you define speed to actually be the magnitude of the vector. However, if speed is taken without direction over time it may become something different. If an object travels along a vector with a negative magnitude its speed will not be negative but its vector magnitude will. Ex: A car travelling in reverse still has a positive speed but a compass will show it to be heading in the opposite direction of travel, a negative vector value...

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.

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

Velocity is a vector. The magnitude of the velocity - its absolute value - is its 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).

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