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# Pls help me with this Physics Problems.. Average Speed..?

1) An airplane takes off at 9:00 am and flies at 300 km/hr until 1:00 pm. At 1 pm, its speed is increased to 400 km/hr, and it maintains this speed until it lands at 3:30 pm. What is the airplane's average speed for the entire flight?

2) A car travels at 100 km/hr for 2h, at 60 km/hr for the next 2 hr and finally at 80 m/s for 1 hr. Find its average speed for the entire 5h.

3) A man drives one-third of the distance home at 25 mi/hr. How fast must he drive the rest of the way in order to average 35 mi/hr for the entire trip?

Thank you very much to those who'll be helping me.. -.-

Relevance
• Dr W
Lv 7

average speed = total distance / total time

1) two intervals. from 9 am to 1 pm, the airplane flies 4 hours at 300 km/hr. speed = distance / time, therefore distance = speed x time = 4 hours x 300 km/hr = 1200 km.

from 1 to 3:30, the plane flies 2.5 hours at 400 km/hr. again d = 2.5 x 400 = 1000 km

average velocity = total distance / total time = (1200 km + 1000 km) / (4 hrs + 2.5 hrs) = 2200 km /6.5 hrs = 338 km/hr

2) similarly

d1 = 2 hrs x 100 km/hr = 200 km

d2 = 2 hrs x 60 km/hr = 120 km

d3 = 1 hr x 80 x km / hr = 80 km

average velocity = 400 km / 5 hours = 80 km/hr

3)

let x = distance home....

interval 1

v = d/t

d1 = 1/3 x

t1 = d1/v1 = (x/3) / (25 mi/hr) = x / (75 mi/hr)

interval 2

d2 = 2/3* x ( this is because you drove 1/3 of x at 25mph and the rest, 2/3 at v2 mph)

t2 = d2/v2 = (2/3 x) / v2 = 2x/3v2

overall..

average v = total distance / total time = x / (x/75 + 2x/3v2)

35 mi/hr = x / (x/75 + 2x/3v2) = x / [ x *(1/75 + 2/3v2)]

35 = 1 / (1/75 + 2/3v2)

rearranging.....

1/75 + 2/(3v2) = 1/35

2/(3v2) = 1/35 - 1/75 = 15/525 - 7/525 = 8/525

1/(3v2) = 4/525

3v2 = 525/4

v2 = 525/12 = 43.75 mph

Using the weighted average

you multiply each velocity by the fraction of time spent at that velocity then add them together for the average

1)300*(4/6.5) + 400*(2.5/6.5) ≈ 338km/h

2) 80m/s = 80m/s*(1/1000)km/m*3600s/h = 288km/h

then

100*2/5 + 60*2/5 + 288*1/5 ≈ 122km/h

3)25*1/3 + v*2/3 = 35

so

v = (35 - 25*1/3)*3/2 = 40mi/h

the end

.

1)

9am-1pm = 4 hrs

1pm-3:30 = 2.5 hrs

300km/hr * 4 hrs = 1200 km

400km/hr *2.5hrs = 1000 km

1200+1000= 2200km traveled from 9am to 3:30 pm

2200km / 6.5 hrs = 338.5 km/hr

2)

100 km/hr * 2 h = 400km

60 km/hr * 2 h = 120km

the 80 m/s must first be converted to km/hr

( 80 m/s /1000 m/km *3600 sec/hr) *1hr = 288 km

400+120+288= 808km / 5hrs = 161.6 km/hr

3)

35mi/hr * 3mi = 105misq/hr

25mi/hr *1 = 25misq/hr

105-25= 80

80misq/hr / 2 miles = 40 mi/hr