a car cover total journey in two equal interval with speed 20km/h and 40km/h then it s average speed is correct answer
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a car cover total journey in two equal interval with speed 20km/h and 40km/h then it s average speed is correct answer
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Answer:
Option - (A) - 80/3 km/hr
Explanation:
Total journey distance = D,
but it is divided into 2 equal intervals. So both intervals are D/2 and D/2
We have 2 time lapse 1st in the 1st d/2=T1 lap and
2nd in the 2nd d/2=T2 lap that is
Total time taken = T1 lap + T2 lap
Now, T1 = ? and T2 = ?
So, T1 = [tex]\frac{d/2}{20}[/tex] = d/40 and
T2 = [tex]\frac{d/2}{40}[/tex] = d/80
So, Total time taken = T1 + T2
=> d/40 + d/80
Average speed = Total distance/Total time taken
=> [tex]\frac{D }{d/40 + d/80}[/tex] => [tex]\frac{D}{2d + d/ 80}[/tex]
=> [tex]\frac{D}{3d/80}[/tex] => 80/3 km/hr
Given : Car travel in two equal half distance
Speed of first half =20 km/hr
Speed of second half = 40 km/hr
To Find : Average speed of the car
Explanation:
Let consider, x= total distance covered by the car,
Time taken to complete the half distance with velocity is 20km/h,
[tex]\[{t_1} = \frac{x}{{2 \times 20}} = \frac{x}{{40}}\][/tex]
The time taken to complete another half distance with velocity is 40km/h.
[tex]\[{t_2} = \frac{x}{{2 \times 40}} = \frac{x}{{80}}\][/tex]
The total time taken, t = [tex]\[{t_1}\][/tex]+[tex]\[{t_2}\][/tex]
[tex]\[t = \frac{x}{{40}} + \frac{x}{{80}} = \frac{{3x}}{{80}}\][/tex] hr
The average speed of the car,
[tex]\[{v_{avg}} = \frac{x}{{3x/80}}\][/tex] km/hr
[tex]\[{v_{avg}} = \frac{{80}}{3}\][/tex] km/hr
Hence the average speed of the car is [tex]\[\frac{{80}}{3}\][/tex] km/hr.