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.
the velocity vector
That's the magnitude of instantaneous acceleration.
Instantaneous velocity is the rate at which an object is moving in a uniform direction, distance per unit time, at any given instant in time. instantaneous acceleration is the rate at which an object's velocity is changing at any given instant in time
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 answer is: Instantaneous Acceleration.
If the displacement of the object (its position) can be described as a functional or algebric equation, you can find the instant speed of this object by calculating the derivative of its displacement equation, knowing that speed is the first derivative of position and acceleration, its second.
That's the magnitude of instantaneous acceleration.
It is the speed or velocity at a particular instant.
Instantaneous velocity is the rate at which an object is moving in a uniform direction, distance per unit time, at any given instant in time. instantaneous acceleration is the rate at which an object's velocity is changing at any given instant in time
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.
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 answer is: Instantaneous Acceleration.
That is called the instantaneous speed.
If the displacement of the object (its position) can be described as a functional or algebric equation, you can find the instant speed of this object by calculating the derivative of its displacement equation, knowing that speed is the first derivative of position and acceleration, its second.
the motion at that instant
The velocity of an object at a particular instant or at a particular point of its path is called instantaneous velocity. In another word, the instantaneous velocity of an object is defined as the limiting value of the average velocity of the object in a small time interval around that instant , when the time interval approaches zero. v = dx/dt , where dx/dt is the differential coefficient of displacement "x" w.r.t. time "t"
No, it is instantaneous acceleration.
Besides obviously distance at any instant, on a connected, continuous distance-time graph, you can obtain instantaneous velocity and instantaneous acceleration.