Question

A particle moves from (2,3) m to (4,2) m. Find the magnitude of displacement.
A. \[\sqrt 3 m\]
B. \[2\sqrt 5 m\]
C. \[\sqrt 5 m\]
D. \[2\sqrt 3 m\]

Answer 1

Hint:Before we start addressing the problem, we need to know about the displacement. When a force is applied, the object changes its position which is known as displacement. Since it is a vector quantity it has both direction and magnitude. Here they have given the coordinates of x and y. using these coordinates we need to find the displacement of a particle.

Formula Used:
To find the magnitude of displacement of particle the formula is,
\[S = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \]
Where, X and y are distance travelled.

Complete step by step solution:
Consider a particle that is moving from one point to another, then we need to find the magnitude of displacement of the particle. We know the formula to find the magnitude of displacement, that is,
\[S = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \]
Substitute the values of
\[S = \sqrt {{{\left( {4 - 2} \right)}^2} + {{\left( {2 - 3} \right)}^2}} \]
\[\Rightarrow S = \sqrt {{{\left( 2 \right)}^2} + {{\left( { - 1} \right)}^2}} \]
\[\therefore S = \sqrt 5 \]
Therefore, the magnitude of the displacement is \[\sqrt 5 \].

Hence, Option C is the correct answer

Note:Remember that the displacement of the particle has both magnitude and direction. So it is a vector quantity. Also, don’t get confused with the terms distance and displacement; they are both different terms. The displacement of the particle will not depend on the path and does not give any information about the path followed but the distance changes according to the path taken by the particle. And, the distance travelled by a particle can never be zero or negative, it is always positive. But if you consider the displacement of a particle, it can be positive, zero or negative.