Question

(1) Define scalar and vector quantities. Identify the following as scalar or vector quantities- mass, velocity, speed, length, distance, displacement, temperature, force, weight, power, work and energy.
(2) The school of a boy from his home is $1km$ to the east. When he reaches back home, he says that he had travelled $2km$ distance but his displacement is zero. Justify your answer

Answer 1

Hint:Here, in the first question we are asked to define and identify the scalar and vector quantities. In the second question we are asked to solve a problem related to the concept of distance and displacement. So we will recall the concept of distance, displacement, scalar quantity and vector quantity.

Complete step by step answer:
(1). Scalar quantities: The quantities which only require magnitude and no direction to describe them are known as scalar quantities.
Vector quantities: The quantities which require both magnitude as well as direction to describe them are called vector quantities.

Here the given quantities are: mass, velocity, speed, length, distance, displacement, temperature, force, weight, power, work and energy.Now let us divide them into two parts: scalar quantities and vector quantities.
Scalar quantity: mass, speed, length, distance, temperature, power, work and energy.
Vector quantity: velocity, displacement, force and weight.

(2). We know that the distance is the actual length of the path travelled between the initial point and final point or position of that moving body. And we also know that the displacement is the linear distance between the initial position and the final position of that moving body.

Now, we all know that a straight line drawn between two points is of least length among all curves joining the two, so the linear distance between two points is the least length of path to be travelled between two points. So, we can say, that distance when it is shortest, becomes displacement. Otherwise, the distance is greater than the displacement.

Distance is a scalar quantity that consists only of magnitude whereas displacement is a vector quantity that means that it consists of magnitude as well as direction.So displacement is given by,
$\text{displacement}=\text{Final Position-Initial Position}$
Here the final position and initial position both are the same. Hence the displacement of the boy is zero. Whereas the distance travelled is $2km$. $1km$ from home to school and $1km$ from school to home back.

Note:We should note that when a vector quantity is multiplied with a scalar quantity, the product obtained is a vector with the same direction but increased magnitude.A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. On the other hand, a vector quantity is defined as the physical quantity that has both magnitude as well as direction like force and weight.