A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as . Notation A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation, A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E. (This is called Newton's notation) Higher time derivatives are also used: the second derivative with respect to time is written as with the corresponding shorthand of . As a generalization, the time derivative of a vector, say: is defined as the vector whose components are the derivatives of the components of the original vector. That is, 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 electric 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. Example: circular motion For example, consider a particle moving in a circular path. Its position is given by the displacement vector , related to the angle, θ, and radial distance, r, as defined in the figure: For this example, we assume that . Hence, the displacement (position) at any time t is given by This form shows the motion described by r(t) is in a circle of radius r because the magnitude of r(t) is given by using the trigonometric identity and where is the usual Euclidean dot product. With this form for the displacement, the velocity now is found. The time derivative of the displacement vector is the velocity vector. In general, the derivative of a vector is a vector made up of components each of which is the