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Q.

Between two points, a car accelerates uniformly at first, then moves with constant speed and finally retards uniformly to rest. If the ratio of times taken is 1 : 4 : 2 and the maximum speed is 70 km/hr find the average speed over the whole journey

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a

33 km/hr

b

44 km/hr

c

55 km/hr

d

66 km/hr

answer is C.

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Detailed Solution

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A to B : (constant acceleration)
$d_{1} = (\frac{0 + v_{m}}{2}) t_{0}$
B to C : (constant velocity)
$d_{2} = v_{m} \times 4 t_{0} = 4 v_{m} t_{0}$
C to D (constant retardation)
$d_{3} = (\frac{v_{m} + 0}{2}) \times 2 t_{0} = v_{m} t_{0}$
$Average speed= \frac{Total distance}{Total time}$
$= \frac{d_{1} + d_{2} + d_{3}}{t_{0} + 4 t_{0} + 2 t_{0}} = 55 km / hr$

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