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Why Is the magnitude of instantaneous velocity always equal to the instantaneous speed?
Wiki User
∙ 9y ago
Yes, it can be. Average speed is the distance traveled divided by the time traveled. Average velocity is the displacement divided by the time traveled. Displacement is change in position, or final position (df) minus initial position (di).
Let's say you traveled from your home to the mall and then back again. The total distance traveled was 30 miles, and the total time driven was 1 hour.
Average speed = distance traveled/time traveled = 30 miles/1 hour = 30mi/hr or 30mph.
Average velocity = (df - di)/time traveled = 0 mile/1 hour = 0 mi/hr or 0mph.*
*In this case the final position and the initial position are the same (your house), so the displacement is zero.
Something to think about: When a Nascar driver races 500 miles around an oval track, his average speed might be 160mph, but his average velocity when he finishes the race is 0mph.
Wiki User
∙ 11y ago
Wiki User
∙ 13y agoYes 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...
Wiki User
∙ 9y agoBecause 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.
Wiki User
∙ 14y agoThere the same, only a direction must be indicated
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When is the average velocity is equal to the instantaneous velocity?
Average velocity equals the average speed if (and only if) the motion is in the same direction. If not, the average speed, being the average of the absolute value of the velocity, will be larger.
When is the instantaneous velocity equal to avg velocity?
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.
Does the instantaneous speed ever equal the magnitude of its average velocity?
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.
How is acceleration similar to speed and velocity?
-- 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.
When will the average acceleration be equal to instantaneous velocity?
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.
When is speed equal to the magnitude of velocity?
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.
Is the magnitude of instantaneous velocity always equal to the instantaneous speed?
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.
When is the average velocity is equal to the instantaneous velocity?
Average velocity equals the average speed if (and only if) the motion is in the same direction. If not, the average speed, being the average of the absolute value of the velocity, will be larger.
When is the instantaneous velocity equal to avg velocity?
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 will the average velocity be equal to instantaneous velocity?
In uniform motion.
The slope of a speed vs time graph is equal to what?
Acceleration.
When is speed equal to magnitude of velocity?
Speed is equal to the magnitude of velocity almost always. Speed is total distance / total time no matter which way the distance goes. Velocity is the distance from a starting point divided by total time.
When average velocity and average speed is equal?
For the instantaneous value of average velocity, average speed and average velocity are equal.
When average velocity is equal to its instantaneous velocity acceleration?
you are still. motion is at rest.
Instantaneous speed at an instant is equal to magnitude of instantaneous velocity at that instant Why is it so?
Instantaneous velocity mean change of displacement in extremely small amount time. (in math way, taking[ lim t--->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.
Is ta possible for an object to have average velocity equal to its instantaneous velocity?
Yes, yes it is
Does the instantaneous speed ever equal the magnitude of its average velocity?
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.
