Position or Location

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Position or Location

The position of a particle is always w.r.t some reference point (origin) of given frame of reference. If the position of a particle w.r.t a given frame of reference is changing with time, the particle is said to be in motion w.r.t the given frame of reference. We represent the position of a particle at any instant by position vector as shown in the figure.

Position-time graph of a particle which is at A at time t1 and at B at time t2.

represent the positions of the particles at t1 and t2, respectively.

Displacement

The change in position vector of the particle for a given time interval is known as its displacement. From the figure, we can observe that the particle is moving from A to B via the path ACB in time interval

Displacement is a vector quantity and its SI unit is a metre.

Distance

The length of the actual path traversed by a particle is termed as distance traveled by a particle in given time interval. For shown situation the distance travelled by particle at the time interval t2 – t1 is the length of the path ACB. Distance is a scalar quantity and its SI unit is a metre.

Comparison between distance and displacement

♦For a moving particle in a given time interval distance there can be many valued functions, but displacement would always be to single valued function.

♦Displacement can decrease with time, but distance would be always +ve.

♦Displacement can decrease with time, but distance can never decrease with time.

♦Distance is always greater than or equal to the magnitude of displacement.

♦Distance is always equal to displacement, only if the particle is moving along a straight line without any change in direction.

Average Speed and Average Velocity

Average speed and average velocity are always defined for a time interval.

Average speed over a time interval is defined as the ratio of total distance travelled in given time interval to the time interval.

Comparisons between vav and →vav can be done in a similar way to what we have done for distance and displacement.

Instantaneous Speed and Instantaneous Velocity

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