question_answer

                               Usually average speed means the ratio of total distance travelled to the total time elapsed. However, sometimes the phrase 'average speed9 can mean the magnitude of the average velocity. Are the two same? Discuss.

Answer:

                It is not correct to say that the average speed of the body is equal to the magnitude of the average velocity because they have got different meanings. As average speed, \[{{\upsilon }_{av}}\] = total distance travelled/time taken and magnitude of average velocity =\[|\overset{\to }{\mathop{{{\upsilon }_{av}}}}\,|\]=| displacement/time I. As, the distance travelled by a moving body is always positive and can never be zero or negative; whereas the displacement of body can be zero, negative or positive. So, distance > displacement. Hence,      \[{{\upsilon }_{av}}\ge |\overset{\to }{\mathop{{{\upsilon }_{av}}}}\,|\]