By "motion", Newton meant the quantity now called momentum, which depends upon the amount of matter contained in a body, the speed at which that body is moving, and the direction in which it is moving. In modern notation, the momentum of a body is the product of its mass and its velocity: p = m v , where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force: F = d p d t . If the mass m does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration: F = m d v d t = m a . As the acceleration is the second derivative of position with respect to time, this can also be written F = m d 2 s d t 2 .