Which of the following statements are incorrect ?(i)i Average velocity is path length divided by time interval.(ii)ii In general, speed is greater than the magnitude of the velocity.(iii)(iii) A particle moving in given direction with a non-zero velocity can have zero speed.(iv)(iv) The magnitude of average velocity is the average speed.A(ii)(ii) and (iii)iiiB(ii)ii and (iv)ivC(i), (iii)i, iii and (iv)ivDAll four
Question
Which of the following statements are incorrect ?(i)i Average velocity is path length divided by time interval.(ii)ii In general, speed is greater than the magnitude of the velocity.(iii)(iii) A particle moving in given direction with a non-zero velocity can have zero speed.(iv)(iv) The magnitude of average velocity is the average speed.A(ii)(ii) and (iii)iiiB(ii)ii and (iv)ivC(i), (iii)i, iii and (iv)ivDAll four
Solution
The correct answer is B(ii)ii and (iv)iv.
Explanation:
(i) Average velocity is displacement (not path length) divided by time interval. Displacement is the shortest distance from the initial to the final position of a point. Hence, the path length is not involved in the calculation of average velocity. So, this statement is incorrect.
(ii) In general, speed is greater than the magnitude of the velocity. This is true because speed is a scalar quantity that refers to "how fast an object is moving," while velocity is a vector quantity that refers to "the rate at which an object changes its position." So, this statement is correct.
(iii) A particle moving in a given direction with a non-zero velocity can have zero speed. This is impossible because speed is the magnitude of velocity. If velocity is non-zero, speed cannot be zero. So, this statement is incorrect.
(iv) The magnitude of average velocity is the average speed. This is not always true. The magnitude of average velocity is equal to the average speed only when the motion is along a straight line without change in direction. So, this statement is incorrect.
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