27. 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.
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Answer:
Net acceleration is due to braking and centripetal acceleration
Due to Braking,
a
T
=0.5m/s
2
Speed of the cyclist, v=27km/h=7.5m/s
Radius of the circular turn, r=80m
Centripetal acceleration is given as:
a
c
=
r
V
2
=(7.5
2
)/80=0.70m/s
2
Since the angle between a
c
and a
T
is 900, the resultant acceleration a is given by:
a=(a
c
2
+a
T
2
)
1/2
a=(0.7
2
+0.5
2
)
1/2
=0.86m/s
2
tanθ=
a
T
a
c
where θ is the angle of the resultant with the direction of the velocity.
tanθ=
0.5
0.7
=1.4
θ=tan
−1
(1.4)=54.56
0
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