How do speed and velocity help to describe and measure motion?

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Velocity describes motion by indicating how fast an object moves and in what direction. Speed is a magnitude of velocity, which indicates only how fast an object moves. Speed shows how much distance is traversed in a given interval of time:

`Speed = (distance)/(time)`

In a general case of motion, when velocity is not constant, an instantaneous velocity is used to describe how fast and where the object is going at a given moment in time. For example, the ball falling down will have a velocity with the magnitude given as a function of time as

`v(t) = 9.8t` (assuming that the gravitational acceleration is 9.8 m/s^2, and neglecting air resistance). The direction of the velocity of the ball is downward, which has to be indicated to complete the description of the motion.

If the instantaneous velocity is known, the acceleration of the object can be found as a derivative of the velocity:

`veca(t) = (dvecv(t))/(dt)` .

If the velocity is known, the displacement also can be calculated as the integral of velocity:

`vecs(t) = int _ (t_0) ^(t_f) vecv(t)dt` . Thus, velocity allows one to measure the displacement of the object during motion between the initial, `t_0` ,  and the final, `t_f` , moments of time.

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