Answer:
Explanation:
Time duration during which acceleration exists in bicycle =
23 / 12 = 1.91 s
Time duration during which acceleration exists in car
= 47 / 8 = 5.875 s
Distance covered by bicycle during acceleration ( t = 1.91 s )
= 1/2 x 12 x (1.91)²
= 21.88 mi
Distance covered by car during this time ( t = 1.91 s )
= 1/2 x 8 x (1.91)²
7.64 mi ,
velocity of car after 1.91 s
= 8 x 1.91 = 15.28 mi/h
Let after time 1.91 , time taken by them to meet each other be t
Total distance covered by cycle = total distance covered by car
21.88 + 23 t = 7.64 + 15.28t + 4 t²
21.88 = 7.64 - 7.72t +4 t²
4 t² -7.72 t -14.24 = 0
t = 2.83 s
Total time taken
= 2.83 + 1.91
= 4.74 s
So after 4.74 s they will meet each other.
b ) Maximum distance occurs when velocity of both of them becomes equal .
Velocity after 1.91 s of bicycle
12 x 1.91 = 23 mi/h
Velocity after 1.91 s of car
8 x 1.91 = 15.28 mi/h . Let after time t , the velocity of car becomes 23
15.28 + 8t = 23
t = .965 s
So after time .965 s , car has velocity equal to that of bicycle.
The bicycle will travel a distance of
= 21.88 + .965 x 23 = 44.075 mi
car will travel a distance of
7.64 + 15.28 x .965 + .5 x 8 x .965²
= 7.64 + 14.75 + 3.72
= 26.11 mi
Distance between car and bicycle
= 44.075 - 26.11 = 17.965 mi
= 17.965 x 1760
= 31618.4 ft.
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