Question

an object moving in a square covers 1.5 rounds find it distance and displacement and it starts from point a ​

Answer 1

Distance :

The numerical measurement of length of the path taken by an object. It is a scalar quantity.

Consider two points A and B located along a straight line. An object can travel multiple ways in order to reach B from A. The path taken by the object is the distance.

Displacement :

Displacement refers to change in an object's position. Unlike Distance, Displacement is a vector quantity.

Let's consider a point P where a person is located. The person goes 5 steps forward, and 2 steps back.

The distance travelled will be 5steps + 2steps, but the displacement will be the distance from the initial position of the object to it's final position which in this case will be 5steps - 2steps.

Answer :

Given :

• An object takes a path shaped as a square of side 5m

Distance :

Distance = 1.5 × Perimeter of the square

$\boxed {\sf Perimeter\:of\:a\:square = 4\times side}$

∴ Distance covered by the object = 1.5 (4×5)

⇒ 1.5 × 20

⇒ 30m

Displacement :

1.5 rounds = 1 full round + half a round.

After completing one full round, the object returns to it's initial position. As we defined Displacement to be the change in an object's position, the object after 1 round does not experience displacement. In other words, the Displacement = 0. The next half round is what we will consider.

As the starting point is A, half of ABCD will be till C.

In ∆ADC,

$\boxed{\sf Displacement = (AD)^{2} + (DC)^{2} = (AC)^{2}}$

$\implies \sf (5)^{2} + (5)^{2} = (AC)^{2}$

$\implies \sf 25 + 25 = (AC)^{2}$

$\implies \sf 50 = (AC)^{2}$

$\implies \sf \sqrt{50} = AC$

⇒√50m = Displacement

∴ The object's displacement is √50m and the distance covered is 30m.