derivative of velocity, , with respect to time and velocity is defined as the derivative of position, , with respect to time, acceleration can be thought of as the second derivative of with respect to : (Here and elsewhere, if motion is in a straight line, vector quantities can be substituted by scalars in the equations.) By the fundamental theorem of calculus, it can be seen that the integral of the acceleration function is the velocity function ; that is, the area under the curve of an acceleration vs. time ( vs. ) graph corresponds to the change of velocity. Likewise, the integral of the jerk function , the derivative of the acceleration function, can be used to find the change of acceleration at a certain time: Units Acceleration has the dimensions of velocity (L/T) divided by time, i.e. L T−2. The SI unit of acceleration is the metre per second squared (m s−2); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second. Other forms An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, although its speed may be constant. In this case it is said to be undergoing centripetal (directed towards the center) acceleration. Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer. In classical mechanics, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net force vector (i.e. sum of all forces) acting on it (Newton’s second law): where is the net force acting on the body, is the mass of the body, and is the center-of-mass acceleration. As speeds approach the speed of light, relativistic effects become increasingly large. Tangential and centripetal acceleration The velocity of a particle moving on a curved path as a function of time can be written as: with equal to the speed of travel along the path, and a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed and the changing direction of , the acceleration of a particle moving on a curved path can be written using the chain rule of differentiation for the product of two functions of time