Question

Side of a square is 4 cm and you make a half round of it find the magnitude of distance travelled and dispalcement

Answer 1

If half round is done moving from along the corners then after half round we reach the corner diagonally opposite to the previous one.

The distance travelled is equal to (4+4=)8 cm.

The displacement though is the length of the diagonal,i.e., \sqrt{4*4+4*4}=\sqrt{32}=5.656 cm  .

Answer 2

ANSWER

Distance travelled = 8 cm

Displacement of body = 4√2 cm

Step By Step Explanation

Plz, refer to the attachment for the diagram.

Now we have :>

Sides of square =AB=BC=CD=AC=4cm

Also, the length of diagonal be AC

Now, according to the question distance traveled by a body

=>AC + AB

=> (4 +4) cm

=> 8cm

Hence the distance traveled is 8cm.

Now for finding the displacement of the body, we need to determine the initial point of origin and final position of the body.

Here,

Let the final position be C.

And the initial position is A.

So we know that the displacement is the shortest distance between the initial and final position.

So, displacement = length of diagonal AC

Now by applying Pythagoras theorem >

$AC = \sqrt{AB^{2} + AC^{2} }$

$\implies AC = \sqrt{4^{2} + 4^{2} }$

$\implies AC = \sqrt{16 + 16 }$

$\implies AC = \sqrt{32}$

$\implies AC = \sqrt{4\times 4\times 2}$

$\implies AC = 4\sqrt{ 2}$cm

Hence the displacement is $4\sqrt{ 2}$cm