# Displacement and Velocity

Suppose two cars A and B start out simultaneously from O. Car A travels towards the north and car B towards the east. After 1 hour, both are at a distance of 50 km from O but their positions with respect to O are not the same. A is 50 km to the north of O and B is 50 km to the east of O.So, we see that in order to completely specify the position of a moving object with respect to a reference point(in this case O), it is necessary not only to specify the distance of the moving body at any time from O, but its direction with respect to O also.

Displacement of a body from a fixed point is its distance from the point in a specified direction.

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Similarly, if we say that a car moves with a speed of 50 km/h from O, we would not know whether we mean car A or car B as their motions with respect to O are quite different. In order to completely specify the motion of a moving body, it is not enough to state its speed only; we also need to specify the direction in which it is moving.

Velocity of a moving body is its speed in a specified direction, or its rate of change of displacement with time (displacement being with respect to a fixed point). Its unit is the same as that of speed. Displacement and velocity are vector quantities.

In case the velocity of the object is changing at a uniform rate, the average velocity is the arithmetic mean of the initial and final velocities. Hence, if â€˜uâ€™ is the initial velocity, â€˜vâ€™ will be its final velocity,

Average velocity v_{av }= (u + v) / 2.