Question

Which of the following is not a vector quantity?
A) Distance
B) Displacement
C) Acceleration
D) Velocity

Answer 1

We need to understand the different physical quantities and the dependence of these quantities on the direction and magnitude of the quantity to classify them as either vector quantity or scalar quantity as required in the solution of the problem.

Complete answer:
We know that the physical quantities which possess both the magnitude and the direction while representing them are called the vector quantities. They need to be expressed in terms of both direction and magnitude to convey the complete sense into the reader. The scalar quantities are those which can be explained just with the magnitude alone.
We are given four physical quantities out of which one is not a vector. Let us discuss each of the quantities and understand the vectors and scalars among them.
Distance: It is the total length of the path taken by a body when moving from one point to another. It is independent of the direction or the initial and final points. It is just the total length without any sense of the direction. It is, therefore, a scalar quantity.
Displacement: It is the shortest possible distance between two given points. The displacement of a particular is independent of the path taken by the moving body. The displacement between two points will be constant no matter how long the body was moving. It is direction dependent and therefore is a vector.
Velocity is the time derivative of the displacement and acceleration is the time derivative of the velocity. Since, the displacement is a vector quantity, the velocity and the acceleration are also vectors.
The required quantity which is not scalar is the distance.

The correct answer is option A.

Note:
The distance and the displacement seem to be the same quantities. Both quantities give the measurement of length. But it is interesting to know that the displacement and distance between the same two points will be entirely different in magnitude.