Need Help finding Instantaenous Velocity

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In summary, instantaneous velocity is the rate at which an object is moving at a specific point in time, taking into account both speed and direction. It differs from average velocity as it provides a more precise measure of an object's motion at a particular moment, while average velocity gives an overall measure over a period of time. To calculate instantaneous velocity, one must know the displacement of an object at a specific point in time, which can be determined through various methods. It is important in physics as it allows for a detailed understanding of an object's motion and can be used to predict future motion. Instantaneous velocity can also be negative, indicating movement in the opposite direction of its positive velocity.
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Bryanaam
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Truck rolls down a Ramp at s(x)=3X^3 + 2x^2 + 4
I need to find Instantaneous velocity at x=4 seconds... The intervals are between 0<x<4. I can't think of the answer.. I know that I'm supposed to get the derivative of it, but then I'm unsure of what to do with that..
 
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Surely, since you refer to the derivative, you know that the derivative is the derivative of the position function with respect to time. Since you are asked for the instantaneous velocity at x= 4 you evaluate the derivative function at x= 4.
 

What is instantaneous velocity?

Instantaneous velocity is the rate at which an object is moving at a specific point in time. It is a measure of both speed and direction and is often represented as a vector quantity.

How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a specific moment in time, while average velocity is the total displacement divided by the total time taken. Instantaneous velocity gives a more precise measure of an object's motion at a particular point, while average velocity gives an overall measure of an object's motion over a certain period.

How can I calculate instantaneous velocity?

To calculate instantaneous velocity, you need to know the displacement of an object at a specific point in time. This can be determined by measuring the distance traveled or by taking the derivative of the position function with respect to time.

Why is instantaneous velocity important in physics?

Instantaneous velocity is important in physics because it helps us understand the motion of objects in detail. It allows us to analyze how objects are moving at any given point in time and can be used to predict future motion.

Can instantaneous velocity be negative?

Yes, instantaneous velocity can be negative. This happens when the object is moving in the opposite direction of its positive velocity. For example, if an object is moving to the left, its velocity would be negative if the positive direction is to the right.

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