Answer:
Usual speed: [tex]500\; {\rm km \cdot h^{-1}}[/tex].
Explanation:
Let the usual duration of the trip be [tex]t[/tex] hours ([tex]t > 0[/tex].) The actual duration of this trip would be [tex](t - (1/2))[/tex] hours.
The usual speed would be:
[tex]\begin{aligned}\frac{1500}{t}\end{aligned}[/tex].
The actual speed would be:
[tex]\begin{aligned}\frac{1500}{t - (1/2)}\end{aligned}[/tex].
The actual speed is [tex]100\; {\rm km \cdot h^{-1}}[/tex] greater than the usual speed. In other words:
[tex]\begin{aligned}\frac{1500}{t - (1/2)} - \frac{1500}{t} = 100\end{aligned}[/tex].
Simplify this equation and solve for [tex]t[/tex] ([tex]t > 0[/tex]):
[tex]\begin{aligned}\frac{15}{t - (1/2)} - \frac{15}{t} = 1\end{aligned}[/tex].
[tex]\begin{aligned}15\, t - 15\, \left(t - \frac{1}{2}\right) = t^{2} - \frac{1}{2}\, t\end{aligned}[/tex].
[tex]\begin{aligned}t^{2} - \frac{1}{2}\, t - \frac{15}{2} = 0\end{aligned}[/tex].
[tex]2\, t^{2} - t - 15 = 0[/tex].
[tex](2\, t + 5)\, (t - 3) = 0[/tex].
Since [tex]t > 0[/tex], the only possible value for [tex]t[/tex] would be [tex]t = 3[/tex].
Thus, the usual duration of this trip would be [tex]3\; {\rm h}[/tex]. The usual speed of this trip would be:
[tex]\begin{aligned}v &= \frac{s}{t} = \frac{1500\; {\rm km}}{3\; {\rm h}} = 500\; {\rm km \cdot h^{-1}}\end{aligned}[/tex].
i. Calculate the average velocity of a motor cycle that travels 72km/hr 20 seconds.
The motorcycle's average velocity will be 20 m/sec. The ratio of the overall distance traveled to the total time taken by the body is the average velocity.
What is average velocity?The average velocity is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.
V= 72km/hr =20 m/sec
Total distance travelled by the motorcycle;
D= v ×t
D=(20 m/sec)×20 sec
D=400 m
The average velocity is:
[tex]\rm v_{avg}=\frac{d_{total}}{t_{total}} \\\\ \rm v_{avg}=\frac{400}{20} \\\\ v_{avg}=20 m/sec[/tex]
Hence,the motorcycle’s average velocity will be 20 m/sec.
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The half-life of radium-226 is 1,600 years and the half-life of carbon-14 is 5,730 years. in one to two sentences, mathematically prove that the decay constant for radium-226 is larger than the decay constant for carbon-14.
please and thank you :)
Explanation:
-226 of 1600
-14 of 5730
-226×16÷100= -36.16
-14×57.3÷100= -802.2
The decay constant for radium-226 is larger than the decay constant for carbon-14.
What is decay constant?Decay constant of radioactive substance is its probability of decay per unit time.
Decay constant for radium-226 is [tex]1.4*10^{-11} /sec[/tex] and for carbon-14 is [tex]3.8*10^{-12} /sec[/tex].
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what is the wavelength of a 28Hz periodic wave at 10 meters per second?
AnswerAnswerAnswerAnswerAnswer:0.3571m
Explanation:
Any sound with a frequency that is too low for humans to hear is called:
Answer:
infrasound
Explanation:
How energy efficiency can reduce energy consumption?
Answer:
The energy efficiency represents the things you can do with some amount of energy, and if you can do more with less, than it reduces the energy consumption.
Explanation:
The answer to this question is actually very simple. Imagine that you use only the half of the energy you produce, an efficiency of 50%. Lets say you need 5kJ, so you would need to produce 10kJ, because you can consume only the half. Now, imagine you increase the efficiency, you use exactly what you can generate, (efficiency of 100%). In this case, if you needed only 5kJ you would need to generate only 5kJ.
Calculate the power if work is 9000 joules and time is 60 seconds
Answer:
150w
Explanation:
power = workdone/time
9000/60
150w
. A 6 ohm resistor is connected to a 15 volt battery.
a. What is the current in the circuit?
b. How much heat is produced in 10 minutes?
Answer:
2.5A , 22500 JOULE
Explanation:
Resistance (R)= 6 ohm
Voltage (V) = 15 volt
a)
Current (I) = ?
From ohm's law,
V=IR
15 = 6*I
I = 2.5 A
b)
time(t) = 10min = 600 second
heat energy (Q) = ?
from Joule's law of heating,
Q = I²*R*t
Q = 2.5² *6*600
Q = 22500 Joule
hence, heat energy produced is 22500 joule.
an airplane carrying out a parcel drops releases a parcel while travelling at a steady speed of 90 m/s at an altitude of 200 m. caculate a)the time taken between the parcel leaving the airplane and it striking the ground b)the horizontal distance travelled by the parcel in this time. c)the speed at which the parcel strikes the ground
a)The time taken between the parcel leaving the airplane, and it's striking the ground will be 6.38 second
c)The speed at which the parcel strikes the ground will be 62.64 m/sec.
What is speed?Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by U for the initial speed while V for the final speed. its SI unit is m/sec.
The given data in the problem is;
Steady speed (V)= 90 m/s
Altitude (h) = 200 m
Time taken (t)=?
horizontal distance travelled(d)=?
Striking speed(V)=?
The striking speed is;
[tex]\rm V^2=U^2+2gh \\\\ V=\sqrt{2gh} \\\\V=\sqrt{2\times 9.81 \times 200} \\\\ V= \sqrt{3924} \\\\ V=62.64 \ m/sec[/tex]
The time taken is found as;
[tex]\rm H = ut + \frac{1}{2} gt^2 \\\\ 200=0+ \frac{1}{2} \times 9.81 \times t^2 \\\\ t=6.38 \ sec[/tex]
Hence, the time taken between the parcel leaving the airplane, and it's striking the ground will be 6.38 second
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What are the properties of mars
Answer:
Explanation:
Its surface is rocky, with canyons, volcanoes, dry lake beds and craters all over it. Red dust covers most of its surface. Mars has clouds and wind just like Earth
Unit Test Review
Active
1
2
3
Which statement best describes heat and thermal energy?
O They are different words for the same thing.
O They represent different concepts.
O Heat is what happens when thermal energy stops moving between substances.
O Thermal energy is what happens when heat moves between substances.
Answer:
option B...
they represent different concept...
i hope this will answer your question
I need help with my homework please? I will give a lot of points and a brainlist.
#1
True
All metals attract magnets
#2
Yes true
Away from magnetic field if you place something it won't attract that
#3
False
Its only possible in case of electromagnetic force fields .
#4
False
Electromagnetic force field
#5
True
Wind turbines are becoming an increasingly popular method of generating a community’s electricity. In wind turbines, wind is used to power electric generators. How will an increase in the use of wind turbines affect the availability of wind in the future?
Answer:
It will not. The thing with wind is as long as the earth rotates and creates and uneven heating of the atmosphere, there will be infinite wind.
Explanation:
pls help in these 2 questions
Answer:
Taking forces along the plane
F cos θ - M g sin θ -100 = M a net of forces along the plane
F = (M a + M g * .5 + 100) / .866 solving for F
F = (80 * 1.5 + 80 * 9.8 * .5 + 100) / .866 = 707 N
F = 707 N acting along the plane
Fn = F sin θ + M g cos θ forces acting perpendicular to plane
Fn = 707 * 1/2 + 80 * 9.8 * .866 = 1030 Newtons forces normal to plane
(this would give a coefficient of friction of 100 / 1030 = .097 = Fn)
What happens to the light when it passes through a converging lens?
a) the light spreads apart
b) the light meets at a point
c) the light is reflected backwards
Answer:
B
Explanation:
the lines WILL meet at a point after crossing focal point
Select the correct location on the image.
Answer:
Violet (Shortest Wave Length)
Explanation:
Violet waves have the highest frequencies. The highest frequencies have the shortest wave length.
How would a parachute fall on the surface of the moon ? Describe. The mass of the Jupiter is
[tex]19 \times 10 ^{27} kg[/tex]
and that of the sun is
[tex]2 \times 10 ^{30} kg[/tex]
If the gravitational force acting between them is
[tex]4.166 \times 10 ^{23} newton[/tex]
calculate the distance between their centres.
Explanation:
the answer is 2.46 × 10^12
What type of monomers make up liquids
Answer:
Carbohydrates - monosaccharides.
Lipids - glycerol and fatty acids.
Nucleic acids - nucleotides.
Proteins - amino acids.
Explanation:
If the half-life of iodine-131 is 8.10 days, how long will it take a 50.00 g sample to decay to 6.25 g?
The time it will take to decay 6.25 grams is 24.4684 days.
What is Half life period?A radioactive substance's half-life is often described as the amount of time it takes for one of its atoms to break apart or transform into another. Ernest Rutherford originally examined the theory in 1907. This is typically represented by the sign Ug or t1/2.
To make the concept clearer, let's use a radioactive element with an hour-long half-life.
Now according to the question the given values are :
T(1/2) for iodine-131 is 5.10 days,
[A]₀ for iodine-131 is 50 grams and,
[A] for iodine-131 is 6.25 grams.
T(1/2)=0.693/k
⇒8.10=0.693/k
⇒k=0.865 [tex]days^{-1}[/tex].
2.303 log [A]₀/[A]= kt
2.303 log(50.00/6.25)= 0.085×t
⇒t=1/0.085×2.303×log8
t=24.4684 days
Hence, the time it will take to decay is 24.4684 days.
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In Alberta, which of the following statements is true?
A. Only adults must be restrained in a vehicle.
B.All children must have booster seats.
C.Babies must be restrained in the front seat only.
D.All occupants must be restrained in a vehicle.
The diagram shows a roller-coaster track. Assume that the system is closed. At point D, the roller-coaster is upside-down and at the top of the vertical loop.
which statement best describes the potential and kinetic energies of a roller-coaster car at point D?
What's the potential energy for
m= 0.5kg
g=98.1
h=1.5
Answer:
7.36 j
Explanation:
PE = m g h so just mutiply the given values .5 * 9.81 *1.5 = 7.36 j
(assuming 1.5 is in meters)
The acceleration due to gravity on earth is 6 times that on the moon. An object weighs 10 kg on Earth. What is the mass on the moon?
Answer:
The object obeys the equation
F = M a on both the earth and the moon (mass does not depend on location)
The problem is a little misleading because if an object has a mass of
10 kg then its weight is 10 kg * 9.8 m/s^2 = 98 Newtons
That means that weight is not expressed in Kg but rather in Newtons
Newton's Law is true on the moon as it is on the earth and F = M a
An object that weighed 10 N on earth would weigh 10 / 6 = 1.67 N on the moon
One must take care in describing a force in units of Newtons not in Kg
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answer:
See below ~
Explanation:
What is happening to each event as the climate changes? Temperatures are increasing, carbon dioxide levels are increasing, the pH of the ocean is decreasing, sea levels are increasing, and the amount of sea ice is decreasing.
Here are orders of answers from start
IncreasingIncreasingDecreasingincreasingdecreasingThe main reason behind these situations is global warming
The emmison of carbon dioxide has increased a lot which is getting harmful day by day
A stone of mass 6kg is released from a height of 30m, calculate the velocity before the impact (take gravity=10m/s)
Answer:
23,49 m/s
Explanation:
Ep= Ek
mgh=mv2/2
6×10×30=6v2/2
1800=6 v2/2
6 v2=3600
v2 =600
v=24,49 m/s
The velocity of the stone, if a stone of mass 6 kg is released from a height of 30 m, is 24.5 m/s.
What is velocity?When something is moving, its velocity shows how quickly its location is changing as seen from a certain angle and as measured by a particular unit of time.
If a point moves a certain distance along its path in a predetermined length of time, its average speed throughout that time is equal to the distance traveled divided by the travel time. For instance, a train traveling 100 km in two hours is doing it at an average speed of 50 km/h.
Given:
The mass of the stone, m = 6 kg,
The height of the release, h = 30 m,
The value of gravity, g = 10 m/s,
Calculate the velocity using energy conservation as shown below,
The kinetic energy = potential energy (Energy conservation)
1/2 × 6 × v² = 6 × 10 × 30
v² = 300 × 2
v² = 600
v = √600
v = 10√6
v = 10 × 2.45
v = 24.49 or 24.5 m/s
Thus, the velocity is 24.5 m/s.
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Transverse waves travel at in a string that is subjected to a tension of if the string is long, what is its mass?
The mass of the string is 0.515 kg.
Calculations and Parameters:Given that:
Tension= 60.5NLength of string= 15.9mv= 43.2 m/sm=?To solve for the mass of the string,
v=√(T/ρ) ,(v=43.2m/s , T=60.5N , L=15.9m )43.2= √(60.5/ρ)60.5/ρ= 1866.24ρ= 0.032418Therefore, the mass would be[tex]15.9*0.03242= 0.515448= 0.515[kg][/tex]
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A nearsighted eye has a far point of 100 cm. Objects further than 100 cm are not seen clearly. A diverging lens is used to permit clear vision of an object placed at infinity. Find the focal length of the lens.
A diverging lens is used to permit clear vision of an object placed at infinity. The focal length of the lens is -100 cm.
What is focal length?The focal length is half of the radius of curvature of the focal lens.
By the lens maker formula,
1/f = 1/v +1/u
where, v is the image distance and u is the object distance.
Give, the object is at infinity and the image must form at 100 cm, the the focal length will be
1/f = 1/ -100 + 1/∞
f = -100 cm
The focal length must be -100 cm for the diverging lens.
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When charging a fully depleted battery with a 220/240-volt charging dock, 2023 leaf s can be fully charged in about ________.
When charging a fully depleted battery with a 220/240-volt charging dock, Nissan LEAF can be fully charged in about 7.5h.
What is battery?It converts the electro chemical energy to the electrical energy when connected across the two ends of the conductor.
The Nissan LEAF comprises of a standard 120-V charging cable. In order to charge it fully, we need a 220/240Volts battery. The time take take n to fully charge is 7.5 hours.
Thus, when charging a fully depleted battery with a 220/240-volt charging dock, Nissan LEAF can be fully charged in about 7.5 h.
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How does the force of gravity
affect objects on Earth?
A. It pulls objects towards the center of Earth.
B. It pushes objects to Earth's surface.
C. It pushes objects away from Earth.
D. It causes objects to bounce off each other.
Answer:
A. It pulls objects towards the center of Earth.
Explanation:
Think about dropping something, where does it go? If you are on earth, this goes down towards the ground due to the attractive force of gravity on every object (to pull everything to center of earth). Like Newton's apple.
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answer:
C. Surface tension
What property of water allowed the paperclip to stay on the top of the water?
Solution:Surface Tension
Explanation:The strong surface tension enables the paper clip float on the water, despite its much higher density which is caused by the cohesive forces between liquid molecules.
What are the basic ingredients needed to form a hurricane? (Select all that apply.)
Question 1 options:
warm water
moist air
high pressure
strong winds that come together from different directions
strong winds that come together from different directions
