Explain clearly, with examples, the distinction between :- magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For simplicity, consider one-dimensional motion only].

Read each statement below carefully and state with reasons, if it is true or false: the average speed of a particle is either greater than or equal to the magnitude of average velocity of the particle over the same interval of time.

Read each statement below carefully and state with reasons, if it is true or false :- the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,

4 gm of sulphur dioxide gas diffuses from a container in 8 min. Mass of helium gas diffusing from the same container over the same time interval is :

Read each statement below carefully and state with reasons, if it is true or false :- the total path length is always equal to the magnitude of the displacement vector of a particle,

On an open ground, a motorist follows a track that turns to his left by an angle of 60^@ after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Define displacement of a particle in linear motion in one dimension. Does it depend upon the origin? Can actual distance travelled by object in the time interval t to t' be greater than or equal to the magnitude of the displacement?

Show that the distance covered by a particle having uniform acceleration in time interval (t'-t) is the area under v - t graph for time t' and t.