# Linear Kinematics

Rest and motion :
Motion means change of position with time. When a body is at rest, its position does not change with time.

But how do we describe the position of a body ? We describe it relative to another body for reference.

Thus, rest and motion are relative. A man sitting in a car moving at 55 mph on a highway is at rest relative to a co-passenger, while he is in motion relative to a person standing on the highway.

In order to describe rest and motion, we select a frame of reference and then describe rest or motion relative to this frame of reference.

Motion can be of two types – translational & rotational.

When a body moves such that it always remains parallel to itself throughout the motion it undergoes translation.

When a body moves so that each point in the body maintains a constant distance relative to a fixed axis in space, the motion is rotation.

Position:

If a particle is moves along a given straight line (assumed along x-axis), its position is represented by the x-coordinate relative to a fixed origin. If the particle moves in a plane (let x-y plane) its position is completely known when the x-and y coordinates of its position are known with respect to the given coordinate axis ox and oy.

Similarly for a particle moving in space, three coordinates (x, y, z) are required.

In vector notation, the position vector OP= r in the three cases mentioned above are represented as

r = xi^ , r = xi^+ yj^ and r = xi^+ yj^ + zk^

Several types of coordinate frames may be used to describe position.

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