Physics

# When will the average acceleration be equal to instantaneous velocity?

345 ###### 2009-07-09 20:29:40

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.

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## Related Questions   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. 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. 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). 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. If the velocity is constant (i.e., there is no acceleration). Terminal velocity is an example, although any constant velocity would fit this description. 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. 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. 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". Only if speed is constant. There can be no acceleration if the average speed is equal to the instantaneous speed. 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.  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.   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. The rate of change of velocity is known as acceleration. Average acceleration is equal to (V2-V1)/(t2-t1). Acceleration is the derivative of the velocity over time graph.  5. A particle is moving along the x-axis. The line graph shows the velocity of the particle over time. When is the instantaneous acceleration of the particle equal to 0? -- 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. You can calculate the instantaneous speed of an object through calculus using derivatives. You can more easily find the instantaneous speed of an object if there is constant acceleration by multiplying the rate of acceleration by time, then adding the initial velocity when time was equal to zero. Yes. (if the initial velocity is zero) if not then velocity = initial velocity + acceleration x time No. acceleration = (final_velocity - initial_velocity) &divide; time

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