Answer to Question #128787 in Mechanics | Relativity for Shilpa S

Question #128787
a train travels 50 km in half hour. it the stops at a station for 20 mins, before traveling for 2 hours at an average speed of 90 km/h what was the trains average speed over the whole journey
1
Expert's answer
2020-08-14T16:01:35-0400

By definition, the average speed is:


vav=ltotTtotv_{av} = \dfrac{l_{tot}}{T_{tot}}

where ltotl_{tot} is the total distance covered by the train in time TtotT_{tot}.

The distance covered during the first part of the journey is 50 km, during the second part is 0 km and during the third part 90km/h2h=18090km/h\cdot 2h = 180 km. Thus:


ltot=50km+0km+180km=230kml_{tot} = 50 km + 0km + 180km = 230km

The time spent on the first part of the journey is 0.5h, on the second part 20/60=1/3 h20/60 = 1/3 \space h and on the third part 2h, The total time is:


Ttot=0.5h+1/3 h+2h=17/6 hT_{tot} = 0.5h + 1/3\space h + 2h = 17/6 \space h

The average speed wil be:


vav=ltotTtot=230km17/6 h81.2 km/hv_{av} = \dfrac{l_{tot}}{T_{tot}} = \dfrac{230km}{17/6\space h} \approx 81.2 \space km/h

Answer. 81.2 km/h.


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