Question

a car travel (1/4) of a circle with radius (r) . find the ratio of the distance to its displacement .

Answer 1

Answer: Distance (D) =

2πr/4 = πr/2 units

displacement = √[(r)²+(r)²] = √2r² = r√2 units

ratio of distance to displacement = (πr/2)/(r√2)

= π/2√2

Explanation:

Answer 2

Answer:

Distance travelled by car =$\frac{1}{4}$ x circumference of circle

                                         =$\frac{2\pi r^{2}}{4}$

The shortest path or distance between two points is called displacement.

In the diagram below, a right angled triangle is formed. The hypotenuse will be the shortest distance i.e. the displacement.

From the Pythagorean theorem ,

$hypotenuse^{2}=base^{2}* height^{2}$

displacement = √[(r)²+(r)²] = √2r² = r√2 units

now,

Ratio of distance to displacement = (πr/2)/(r√2)

              on simplifying                   = π/2√2

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