Third Derivative of Distance-Time Function - What is it Called?

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In summary, the third derivative of the distance-time function is the rate of change of the acceleration with respect to time. Its formula is d^3x/dt^3, and it is used in physics to analyze the motion of objects and predict future motion. It is also known as the jerk and is used in various real-world applications such as engineering, physics, and sports.
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bomba923
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Hey um, what's the third derivative of the distance-time function?

d'(t)=velocity
d''(t)=v'(t)=acceleration
d'''(t)=v''(t)=a'(t)=??

I remember there was a special name for this function--but i can't remember what was; what is it called?
 
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Jerk (or alternatively jolt).
 
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The third derivative of the distance-time function is known as the jerk, or the rate of change of acceleration. It measures how quickly the acceleration is changing over time.
 

FAQ: Third Derivative of Distance-Time Function - What is it Called?

What is the concept of the third derivative of the distance-time function?

The third derivative of the distance-time function is the rate of change of the acceleration with respect to time. It measures how quickly the acceleration is changing over time.

What is the formula for calculating the third derivative of the distance-time function?

The formula for calculating the third derivative of the distance-time function is d^3x/dt^3, where x represents the distance and t represents time. This is also known as the third derivative with respect to time.

What is the significance of the third derivative of the distance-time function in physics?

In physics, the third derivative of the distance-time function is used to analyze the rate of change of the acceleration, which is a key factor in understanding the motion of objects. It provides information about how quickly the acceleration is changing, which can help predict the future motion of an object.

What is the name of the third derivative of the distance-time function?

The third derivative of the distance-time function is called the jerk. It is a term coined by physicist Sir James Jeans, and it refers to the sudden changes or "jerks" in acceleration that can occur in a moving object.

How is the third derivative of the distance-time function used in real-world applications?

The third derivative of the distance-time function is used in various fields such as engineering, physics, and mathematics. It is used to study the motion of objects, design efficient and smooth movements in machines, and analyze changes in acceleration in sports and other activities.

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