A person travels by car from one city to another with different constant speeds between pairs of cities

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A person travels by car from one city to another with different constant speeds between pairs of cities

[From: ] [author: ] [Date: 11-12-20] [Hit: ]

6 mors = 32.6536 km - - - Ans.......

So Vavg = S/T = (V1t1 + V2t2 + V3t3)/(t1 + t2 + t3) = (50*55 + 75*13 + 55*30)/(55 + 13 + 30) = 54.85 kph ANS a).

NOTE: No unit conversions needed as the time units in the numerator and denominator cancel out. This is a weighted average and the weights are t/T.

S = Vavg T = 54.85*(55 + 13 + 30)/60 = 89.59 km ANS b)

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Data:
t1 = 55 min = 3300 sec

v1 = 50 km/h = 13.88 m/s

t2 = 13 min = 780 sec

v2 = 75km/h = 20 .83 m/s

t3 = 30 min = 1800 sec

v3 = 55km/h = 15.27 m/s

(a) v = ?
(b) s = ?

Sol: (a)
Average speed is given by:

V = (sum of all speeds) / (total no: of speeds)

V = (13.88 + 20.83 + 15.27) / (3)

V = (49.98) / (3)

V = 16.66 m/s - - - Ans.

(c) The average time is calculated as:

t = (t1 + t2 + t3) / 3

t = (3300 + 780 + 1800) / 3

t = 5880 / 3

t = 1960 sec

for average speed, distance is calculated as:

s = v t

s = 16.66 * 1960

s = 32653.6 m

or

s = 32.6536 km - - - Ans.

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