Question

Supriya is cycling on a circular track. She starts from point A and reaches point B in 20
minutes.
(4 marks)
a) If the speed of her bicycle is 20 km/hr, calculate the distance covered by her and her
displacement as she cycles from point A to B?
b) She cycles from point B back to point A in another 40 minutes. Calculate her average
speed and average velocity in the entire journey from point A to point B and back to
point A.
1
A
B​

Answer 1

Solution :-

→ Speed from A to B = 20 km/h .

→ Time taken = 20 minutes .

so,

→ Distance from A to B = S * T = 20 * (20/60) = (20/3) km.

also,

→ Displacement = Final position - Initial position = Shortest distance between A and B = Diameter.

then,

→ Distance covered = Circumference of half circle .

therefore,

→ π * r = (20/3)

→ r = (20/3) * (1/3.14) = 20/9.42 = 2.12 m.

hence,

→ Displacement = 2 * r = 2 * 2.12 = 4.24 m.

now,

→ Speed from B to A = 20 km/h

→ Time taken = 40 minutes .

so,

→ Distance from B to A = S * T = 20 * (40/60) = (40/3) km.

then,

→ Average speed = Total distance / Total time = {(20/3) + (40/3)} / (20 + 40) = (60/3) / (60/60) = 20 km/h .

also,

→ Average velocity = Net displacement / Total time = 0 / 60 minutes = 0 .

Answer 2

Given : Supriya is cycling on a circular track.

She starts from point A and reaches point B in 20 minutes.

Speed of her bicycle is 20 km/hr,

She cycles from point B back to point A in another 40 minutes.

To Find :  a) the distance covered by her and her displacement as she cycles from point A to B

b) average speed and average velocity in the entire journey from point A to point B and back to point A.​

Solution :

starts from point A and reaches point B in 20 minutes.

Time = 20 minutes = 20/60 hrs = 1/3  hrs

Speed of Bicycle  = 20 km/hr

Distance covered = 20 * 1/3  = 20/3  = 6.67  km

Displacement will be Diameter  = 2 × ( Radius)

π (radius)  = 20/3    ( semi circle circumference )

=> radius = 20/3π

Diameter   = 2 ×  20/3π  = 40/3π   =  4.24  km

She cycles from point B back to point A in another 40 minutes.

=> Total time = 20 + 40 = 60 minutes = 1 hr

Total Distance = 2 x 20/3  = 40/3 km

Average speed = 40/3  km/hr  = 13.33 km/hr

Return to same point hence displacement = 0  km

average velocity = 0/1 = 0    km/hr

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