Question

If speed is a scalar quantity, then average speed
A). Is a vector quantity
B). May be a scalar or a vector quantity
C). Is also a scalar quantity
D). Is neither a scalar nor a vector quantity

Answer 1

Hint: A scalar quantity is the one which has magnitude only and vector quantity has both magnitude and direction. The formula for average speed is given as the ratio of total distance travelled and the total time taken.

Complete step by step answer:
Scalars are those physical quantities that have magnitude only and no direction. Speed is a scalar quantity given by the ratio of distance upon time where both distance and time are scalar quantities. So, the ratio of two scalar quantities is also a scalar quantity.
Vectors are those physical quantities that have both magnitude and direction, for e.g. Velocity is a vector quantity which is the ratio of displacement upon time, here displacement is a vector quantity and time is a scalar quantity. Note that the ratio of vectors by scalar is a vector quantity.
Now, Average speed is given by:
\[{{\text{S}}_{\text{avg}}}\text{=}\dfrac{{{\text{D}}_{\text{Total}}}}{{{\text{T}}_{\text{Total}}}}\]
Here total distance and total time both are scalar quantities therefore, average speed is also a scalar quantity with magnitude only.
Hence, the correct answer is option C. Is also a scalar quantity.

Note: When a vector is multiplied by a scalar it becomes a vector quantity with a magnitude that is scalar times the magnitude of the vector and it acts in the direction of the vector itself. The unit of the new quantity formed after the product would not be the same as the unit of vector.
For e.g.: The product of \[\overrightarrow{F}=100N\] due North and \[t=10\sec \] will give:
\[t\overrightarrow{F}=1000N-\sec \] due North