Time Derivative - Use in Physics

Use in Physics

Time derivatives are a key concept in physics. For example, for a changing position, its time derivative is its velocity, and its second derivative with respect to time, is its acceleration. Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk. See motion graphs and derivatives.

A large number of fundamental equations in physics involve first or second time derivatives of quantities. Many other fundamental quantities in science are time derivatives of one another:

• force is the time derivative of momentum
• power is the time derivative of energy
• electrical current is the time derivative of electric charge

and so on.

A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing with such a derivative, both magnitude and orientation may depend upon time.