Question

A particle moves from (2,3) m to (4,1) m . The magnitude of displacement is
1) 2m 2) 2√3m 3) 2√2m 4) 3√2m

Answer 1

Answer:

2 root 2 m is the correct answer

Answer 2

Given: Initial position of the particle is (2,3)m

The final position of the particle is (4,1)m

To Find: Magnitude of displacement

Solution:

Displacement of a body is the change in its position with respect to its initial position.

Displacement is a vector quantity.

Initial position vector =( 2i + 3j + 0k)m

Final position vector = (4i + 1j + 0k)m

Displacement vector = Final position vector - Initial position vector

                                   = 4i + 1j + 0k - (2i + 3j + 0k)

                                   = 4i - 2i + 1j - 3j

                                   = (2i - 2j)m

The magnitude of a vector = $\sqrt{x^{2} + y^{2} + z^{2} }$, where x, y, and z are the x, y, and z components of the vector.

The magnitude of displacement vector = $\sqrt{2^{2} + (-2)^{2} }$

                                                                  = $\sqrt{4+4}$

                                                                  = $\sqrt{8}$

                                                                  = 2$\sqrt{2 }$m

Therefore, the magnitude of displacement of the particle is  2$\sqrt{2 }$m.