Q: In calculus what is the instantaneous acceleration?

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if under uniform acceleration or deceleration v = u + (a*t) where: v = instantaneous velocity u = initial velocity a = acceleration (negative if decelerating) t = time elapsed

Suppose you accelerate in your car from stopped to 50 km.hr-1. When you were stopped your instantaneous speed was zero. At the end of the period of acceleration your instantaneous speed was 50 km.hr-1. If your rate of acceleration was constant then your average speed was 25 km.hr-1.

you are still. motion is at rest.

Gravity is a force, which means that it has a corresponding acceleration (rate of rate of change). Because calculus is the study of rates of change, accelerations are studied in calculus.

Measures of motion (displacement, velocity, acceleration) and forces are all vectors so any study involving these would require vector calculus.

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To find the instantaneous acceleration of a particle, you would need to know the rate of change of its velocity at that specific moment in time. This can be calculated using calculus by taking the derivative of the velocity function with respect to time. The instantaneous acceleration provides information about how the velocity of the particle is changing at that precise instant.

Instantaneous acceleration at any point on a velocity-time graph can be determined by calculating the slope of the tangent line at that specific point. A steeper slope represents a higher acceleration, while a shallower slope indicates a lower acceleration.

If the average acceleration is zero, it means that the object's velocity is not changing over time. Since instantaneous acceleration is the acceleration at a specific moment in time, it can still have a non-zero value depending on the instantaneous velocity of the object at that moment.

There are, of course, several formulae that involve acceleration. The basic definition of acceleration is: acceleration = delta velocity / delta time, that is, to get average acceleration, divide the difference of velocity by the time that passed. The same formula also gives you the instant acceleration, if the acceleration is constant. If you want to get instantaneous acceleration, and the acceleration changes, then you need calculus: acceleration = dv / dt (that is, take the derivative of the velocity).

To find the instantaneous angular acceleration, you need to know the time rate of change of the instantaneous angular velocity. Without this information, you cannot calculate the instantaneous angular acceleration at t=5.0s.

Average acceleration is the change in velocity over a specific time interval, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration gives an overall picture of how velocity changes over time, while instantaneous acceleration gives the acceleration at a precise point in time.

no.

No, average acceleration is the overall change in velocity over a specific time interval, whereas instantaneous acceleration is the acceleration at a specific moment in time. For a uniformly accelerated car, the average acceleration is constant over the entire interval, but the instantaneous acceleration can vary at different points during that interval.

instantaneous acceleration is the acceleration at one point. yeah, it's true

Instantaneous acceleration and average acceleration are the same when an object's acceleration is constant over the entire time interval being considered. This means that the object's velocity is changing at a constant rate, resulting in both the instantaneous and average accelerations being equal.

Instantaneous acceleration is the rate of change of velocity at a specific moment in time. It indicates how quickly the velocity of an object is changing at that instant. It is typically calculated as the derivative of velocity with respect to time.

The direction of instantaneous acceleration is in the direction of the change in velocity at that moment. If the velocity is increasing, the acceleration is in the same direction as the velocity. If the velocity is decreasing, the acceleration is in the opposite direction of the velocity.