Question

Q10.An object moves along the grid through the points A,B,C,D,E,and
F as shown below.
a)Find the distance covered by the moving object.
b)Find the magnitude of the displacement of the object.

Answer 1

Hello!

Let the distances travelled  d(AB) , d(BC) , d(CD) , d(DE) , d(EF).

a) We've to find the distance travelled from A to F. And each block is of 0.5 km.

By definition, Distance is the total path length covered by a moving body in certain time.

a) So, Distance covered = d(AB) + d(BC) + d(CD) + d(DE) + d(EF)

                                    = (6*0.5) + (2*0.5) + (3*0.5) + (1 * 0.5) + (1*0.5)

                                    = 3 + 1 + 1.5 + 0.5 + 0.5

Thus, distance covered = 6.5 km

b) By definition, Displacement is defined as the shortest distance travelled by a moving body from its initial position to final position.

The attached image depicts the displacement. (with green colour line)

Here, A is initial point and F is final point.

So, to find out displacement we draw a perpendicular FX to AB so as to form a right angled triangle.

And from pythagoras theorem, we'll find out the displacement AF.

$AF = \sqrt{(AX)^2 + (FX)^2}\\\\AF = \sqrt{(0.5\times4)^2 + (0.5 \times 3)^2}\\\\AF = \sqrt{4+2.25}\\\\AF = \sqrt{6.25}\\\\AF = 2.5 \ km$

Hence, Displacement is 2.5 km.

Answer 2

Answer:

a)distance = AB + BC + CD + DE + EF = 3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km

b) Initial point is A and the final point is F, hence the magnitude of the displacement is equal to the distance AF which is calculated by applying Pythagora's theorem to the triangle AHF as shown in the figure below