Question

An object moves from point A to C along the rectangle . Find the magnitude of the displacement of the object
{ A-B=12 cm
B-C=5 cm
C-D=12 cm
D-A=5 cm
it is a rectangle AB and CD length are same (12cm) & BC and DA breadth are same (5cm) ​

Answer 1

Answer:

13 cm

Explanation:

As per the provided information in the given question, we have :

• An object moves from point A to C along the rectangle.
• Length [ AB & CD ] is 12 cm and breadth [ BC & DA ] is 5 cm.

We are asked to calculate his displacement.

Displacement is the shortest distance from initial to the final position of the body. The shortest distance between two points is always a straight line. Here, object's initial position is A and final position is C. Thus, as the shortest distance between two points is always a straight line, so the diagonal of the rectangle (AC) will be the displacement.

Now, as angles of a rectangle measure 90° each. So, by using the Pythagoras property,

$\longmapsto \rm { \ell^2 + b^2 = (Diagonal)^2}$

$\longmapsto \rm { (AB)^2 + (BC)^2 = (AC)^2}$

$\longmapsto \rm { (12 \; cm)^2 + (5 \; cm)^2 = (AC)^2}$

$\longmapsto \rm { 144 \; cm^2 + 25 \; cm^2 = AC^2}$

$\longmapsto \rm { 169 \; cm^2 = AC^2}$

$\longmapsto \rm { \sqrt{169 \; cm^2} = AC}$

$\longmapsto \bf { 13 \; cm= AC}$

∴ Magnitude of the displacement is 13 cm.

$\rule{200}2$

More Information :

• Displacement is the shortest distance from initial to the final position of the body.
• The shortest distance between two positions is always a straight line.
• It is a vector quantity.
• Its SI unit is m.
• It is denoted by v.
• Displacement = Velocity × Time