Question

Which of the following is not a vector quantity?
A. Force
B. Torque
C. Velocity
D. Speed

Answer 1

Hint: Recall the definition of a vector quantity. Recall that it has both magnitude and direction.

Complete step by step answer:
In physics, a vector quantity is any physical quantity that has both magnitude and direction. A vector quantity differs from a scalar quantity primarily in the fact that a scalar quantity has only magnitude but no direction.
Force (F) is a vector quantity since it has both magnitude and direction. Its magnitude is the product of the mass (m) of a body and the acceleration (a) attained by the body due to the force being applied on it. It has the same direction as the acceleration of the body.
$\overrightarrow{F}=m\overrightarrow{a}$
Torque (τ) is a vector quantity since it has both magnitude and direction. Its magnitude is the product of the radial distance (r) from the axis or point of rotation of the body and a force (F) applied on it. It has a direction that is perpendicular to the plane containing the force and radial distance vectors.
$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$
Velocity (v) is a vector quantity since it has both magnitude and direction. Its magnitude is the ratio of the displacement (d) of an object to the time (t) taken by the object to achieve that displacement. It has the same direction as the displacement.
$\overrightarrow{v}=\dfrac{\overrightarrow{d}}{t}$
However, speed (s) is not a vector quantity. It has only magnitude but no direction. So, it is a scalar quantity. Its magnitude is the ratio of the distance (d) covered by a body to the time (t) taken by the body to cover that distance.
$s=\dfrac{d}{t}$
So, the correct option is D) speed.

Note: Such type of problems can be easily solved if one remembers the vectorial equation of vector quantities, as given above and not just the mathematical equations for calculating the magnitudes. For example try to remember for velocity that
$\overrightarrow{\text{velocity}}\text{=}\dfrac{\overrightarrow{\text{displacement}}}{\text{time}}$
And not $\text{velocity=}\dfrac{\text{displacement}}{\text{time}}$
Some quantities like work appear to be vectors but are actually scalar. If proper vectorial equations are used for understanding the definitions, then such confusion will not take place.