1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
garri49 [273]
3 years ago
12

A train traveled from Station A to Station B at an average speed of 80 kilometers per hour and then from Station B to Station C

at an average speed of 60 kilometers per hour. If the train did not stop at Station B, what was the average speed at which the train traveled from Station A to C?
(1) The distance that the train traveled from Station A to Station B was 4 times the distance that train traveled from Station B to Station C.
(2) The amount of time it took to the train to travel from Station A to Station B is 3 times the amount of time that it took the train to travel from Station B to Station C.
Physics
1 answer:
Vinil7 [7]3 years ago
4 0

Answer:

1)

75 kmh⁻¹

2)

75 kmh⁻¹

Explanation:

1)

v_{ab} = Speed of train from station A to station B = 80 kmh⁻¹

d_{ab} = distance traveled from station A to station B

t_{ab} = time of travel between station A to station B

we know that

Time = \frac{distance}{speed}

t_{ab} = \frac{d_{ab}}{v_{ab}} = \frac{d_{ab}}{80}

d_{bc} = distance traveled from station B to station C

v_{bc} = Speed of train from station B to station C = 60 kmh⁻¹

t_{bc} = \frac{d_{bc}}{v_{bc}} = \frac{d_{bc}}{60}

Total distance traveled is given as

d = d_{ab} + d_{bc}

Total time of travel is given as

t = t_{ab} + t_{bc}

Average speed is given as

v_{avg} = \frac{d}{t} \\v_{avg} = \frac{d_{ab} + d_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{d_{ab} + d_{bc}}{(\frac{d_{ab}}{80} ) + (\frac{d_{bc}}{60} ) }

Given that :

d_{ab} = 4 d_{bc}

So

v_{avg} = \frac{4 d_{bc} + d_{bc}}{(\frac{4 d_{bc}}{80} ) + (\frac{d_{bc}}{60} ) }\\v_{avg} = \frac{4 + 1}{(\frac{4 }{80} ) + (\frac{1}{60} ) }\\v_{avg} = 75 kmh^{-1}

2)

v_{ab} = Speed of train from station A to station B = 80 kmh⁻¹

t_{ab} = time of travel between station A to station B

d_{ab} = distance traveled from station A to station B

we know that

distance = (speed) (time)

d_{ab} = v_{ab} t_{ab}\\d_{ab} = 80 t_{ab}

d_{bc} = distance traveled from station B to station C

v_{bc} = Speed of train from station B to station C = 60 kmh⁻¹

t_{bc} = time of travel for train from station B to station C

we know that

distance = (speed) (time)

d_{bc} = v_{bc} t_{bc}\\d_{bc} = 60 t_{bc}

Total distance traveled is given as

d = d_{ab} + d_{bc}\\d = 80 t_{ab} + 60 t_{bc}

Total time of travel is given as

t = t_{ab} + t_{bc}

Average speed is given as

v_{avg} = \frac{d}{t} \\v_{avg} = \frac{d_{ab} + d_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{80 t_{ab} + 60 t_{bc}}{t_{ab} + t_{bc}}

Given that :

t_{ab} = 3 t_{bc}

So

v_{avg} = \frac{80 t_{ab} + 60 t_{bc}}{t_{ab} + t_{bc}}\\v_{avg} = \frac{80 (3) t_{bc} + 60 t_{bc}}{(3) t_{bc} + t_{bc}}\\v_{avg} = \frac{(300) t_{bc}}{(4) t_{bc}}\\v_{avg} = 75 kmh^{-1}

You might be interested in
Suppose the number of coils in the solenoid of an electromagnet is increased. What happens to the electromagnet?
Akimi4 [234]

Answer:

Its strength becomes greater.

Explanation:

5 0
2 years ago
Read 2 more answers
Which astronomer gave his name to a telescope launched into space in 1990?
Mnenie [13.5K]

Answer:

Edwin Hubble

Explanation:

5 0
3 years ago
Recalculate 100 km/h to m/s
qwelly [4]

= 27.777

Explanation:

A kilometer has 1,000 meters, and an hour has 3,600 seconds, so 100 kilometers per hour is: 100 x 1,000 / 3,600 = 27.777... m/s.

4 0
3 years ago
In a $100$ meter track event, Alice runs at a constant speed and crosses the finish line $5$ seconds before Beatrice does. If it
Liono4ka [1.6K]

Answer:

10s

Explanation:

If it took Beatrice 25 seconds to complete the race

Distance = 100 meter

Beatrice speed = 100/25

                          = 4m/s

If Alice runs at a constant speed and crosses the finish line $5$ seconds, she must have completed the race in 20s (25 -5).

Her speed where constant

= 100/20

= 5 m/s

It would take Alice

= 50/5

= 10s

It would take Alice 10s to run $50$ meters.

5 0
3 years ago
The time delay between transmission and the arrival of the reflected wave of a signal using ultrasound traveling through a piece
Brilliant_brown [7]

Answer:

10.01 cm

Explanation:

Given that,

The time delay between transmission and the arrival of the reflected wave of a signal using ultrasound traveling through a piece of fat tissue was 0.13 ms.

The average propagation speed for sound in body tissue is 1540 m/s.

We need to find the depth when the reflection occur. We know that, the distance is double when transmitting and arriving. So,

v=\dfrac{2d}{t}\\\\d=\dfrac{vt}{2}\\\\d=\dfrac{1540\times 0.13\times 10^{-3}}{2}\\\\d= $$0.1001\ m

or

d = 10.01 cm

So, the reflection will occur at 10.01 cm.

8 0
2 years ago
Other questions:
  • A particle travels 15 times around a 10-cm radius circle in 42 seconds. what is the average speed (in m/s) of the particle?
    11·1 answer
  • Near the end of a marathon race, the first two runners are separated by a distance of
    15·1 answer
  • We divide the electromagnetic spectrum into six major categories of light, listed below. Rank these forms of light from left to
    12·1 answer
  • How to improve in physics?
    15·1 answer
  • HELP A car traveling at 4m/s accelerates at a rate of .80m/s2 for 1.8s. What is its final velocity?
    8·2 answers
  • If the gap between C and the rigid wall at D is initially 0.15 mm, determine the magnitudes of the support reactions at A and D
    6·1 answer
  • The force that makes objects keep traveling is ____.
    12·2 answers
  • それで、私はヘビと一緒に座っていました、そしてこれが起こりました、私のヘビは本当に奇妙に行動していたので私は本当に混乱したようでした、私のヘビは本当に奇妙に行動していたので、私はオーロラのようでした、やめてください。それから彼女は私をすべて奇妙に見たので私
    10·1 answer
  • If a train has 1,450 kg of momentum and is traveling at 40 m/s ¿what is the mass of tren?
    12·1 answer
  • An object has a mass of 7g and a volume of 14cm. What is the density
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!