Question

Under what condition is the magnitude of the average velocity of an object equal to its average speed?
(A). Body moves along a curved path
(B). Body moves along the straight path
(C). Both A and B
(D). None of the above

Answer 1

Hint: Write the formula for average velocity and average speed from their definition. Compare both formulae. Both the formulae give the same answer. The main difference between speed and velocity is speed is a magnitude quantity only while velocity is a quantity of both magnitude and direction.

Complete answer step by step:
Average speed:
The average speed of a body is defined as the total distance covered by a body divided by total time taken to cover that distance.
$\text{Average speed = }\dfrac{\text{Total distance covered}}{\text{Total time taken}}$
Average velocity:
The average velocity of a body is defined as the total displacement of a body divided by the total time taken.
$\text{Average velocity = }\dfrac{\text{Total displacement}}{\text{Total time taken}}$
By looking at both the formulae we can say that the magnitude of average velocity and average speed will be equal, when the total distance is equal to total displacement. This is possible only when the body moves in a straight line. Therefore, under the condition that the body is moving in a straight line, the magnitude of the average velocity of an object is equal to its average speed.
Hence the correct answer is option B.

Additional Information:
Speed is scalar quantity whereas velocity is a vector quantity. The S.I. unit of both speed and velocity is $\text{m}{{\text{s}}^{\text{-1}}}$.

Note: Note that average speed and velocity are different than the instantaneous speed and velocity. Displacement is defined as the shorter distance between two points, which is a straight line distance. Thus if a body is moving along the straight line then its displacement is the same as distance covered by it. Distance is the total path covered by the body.