An engineer measures the velocity of a remote-controlled cart on a straight track at regular time intervals. The data are shown in the graph above. During which of the following time intervals did the cart return to its position at time t=0 s?
A. 7 s ≤ t < 10 s
B. 10 s ≤ t < 12 s
C. 5 s ≤ t < 6 s
D. 3 s ≤ t < 5 s
Answers
Answer:
A. 7 s ≤ t < 10 s
Explanation:
From Definite Integral Theory and Mechanical Physics we remember that change in position is represented by sum of areas below the curve. According to the graphic, we see that the following condition must be satisfied:
[tex]A_{1}+A_{2} = 0[/tex] (1)
Where:
[tex]A_{1}[/tex] - Change in position from [tex]t = 0\,s[/tex] and [tex]t = 3\,s[/tex], measured in meters.
[tex]A_{2}[/tex] - Change in position from [tex]t = 5\,s[/tex] and [tex]t = T[/tex], measured in meters.
By definitions of triangle, we expand the equation above:
[tex]\frac{1}{2}\cdot (3\,s)\cdot \left(1.2\,\frac{m}{s} \right) -\frac{1}{2}\cdot (T-5\,s)\cdot v = 0\,m[/tex]
[tex]1.8\,m-0.5\cdot T \cdot v +2.5\cdot v = 0[/tex]
And the time is now cleared:
[tex]1.8\,m+2.5\cdot v = 0.5\cdot T\cdot v[/tex]
[tex]T = \frac{1.8+2.5\cdot v}{0.5\cdot v}[/tex]
Where:
[tex]v[/tex] - Final velocity of the cart, measured in meters per second.
[tex]T[/tex] - Time, measured in seconds.
If we know that [tex]v = 1\,\frac{m}{s}[/tex], then the intended instant is:
[tex]T = \frac{1.8+2.5\cdot (1)}{0.5\cdot (1)}[/tex]
[tex]T = 8.6\,s[/tex]
The value does not coincide with the time from the graph.
If we know that [tex]v = 1.5\,\frac{m}{s}[/tex], then the intended instant is:
[tex]T = \frac{1.8+2.5\cdot (1.5)}{0.5\cdot (1.5)}[/tex]
[tex]T = 7.4\,s[/tex]
This value does not coincide with the time from the graph.
If we know that [tex]v = 1.1\,\frac{m}{s}[/tex], then the intended instant is:
[tex]T = \frac{1.8+2.5\cdot (1.1)}{0.5\cdot (1.1)}[/tex]
[tex]T = 8.273\,s[/tex]
This results offer a reasonable approximation, which that the correct answer is A.
The car will return to its position at the time interval of 7 s ≤ t < 10 s. Hence, option (A) is correct.
The change in position is represented by sum of areas below the curve. According to the graphic, we see that the following condition must be satisfied:
A + A' = 0 ..................................................(1)
A is the change in position from t = 0 and t = 3 s, measured in metres.
A' is the change in position from t = 5 and t = T s, measured in metres.
As per the triangle law,
1/2 ×(3 s)(1.2) - 1/2 ×(T - 5)v = 0
1.8 - 0.5T(v) +2.5(v) =0
T = (1.8 + 2.5v)/ (0.5v)
Here, v is the final velocity of cart.
For v = 1 m/s, we have,
T = (1.8 + 2.5(1))/ (0.5(1))
T = 8.6 s
Since, the values do not coincide with the time from the graph, so taking another value, v = 1.5 m/s to obtain the time as,
T = (1.8 + 2.5(1.5))/ (0.5(1.5))
T = 7.4 s
This value does not coincide with the time from the graph. If we know that , v = 1.1 m/s, then the intended instant is:
T = (1.8 + 2.5(1.1))/ (0.5(1.1))
T = 8.273 s
Thus, we can conclude that the car will return to its position at the time interval of 7 s ≤ t < 10 s. Hence, option (A) is correct.
Learn more about the speed-time graph here:
https://brainly.com/question/19375328
Related Questions
A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 G to 1.60 M in 0.99 s. What is the resulting induced current if the loop has a resistance of 1.20 Ω?
Answers
Complete Question
A flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 1.60 T in 0.99 s. What is the resulting induced current if the loop has a resistance of [tex]1.20 \ \Omega[/tex]
Answer:
The current is [tex]I = 0.0007 41 \ A[/tex]
Explanation:
From the question we are told that
The area is [tex]A = 8.00 \ cm^2 = 8.0 *10^{-4} \ m^2[/tex]
The initial magnetic field at [tex]t_o = 0 \ seconds[/tex] is [tex]B_i = 0.500 \ T[/tex]
The magnetic field at [tex]t_1 = 0.99 \ seconds[/tex] is [tex]B_f = 1.60 \ T[/tex]
The resistance is [tex]R = 1.20 \ \Omega[/tex]
Generally the induced emf is mathematically represented as
[tex]\epsilon = A * \frac{B_f - B_i }{ t_f - t_o }[/tex]
=> [tex]\epsilon = 8.0 *10^{-4} * \frac{1.60 - 0.500 }{ 0.99- 0 }[/tex]
=> [tex]\epsilon = 0.000889 \ V[/tex]
Generally the current induced is mathematically represented as
[tex]I = \frac{\epsilon}{R }[/tex]
=> [tex]I = \frac{0.000889}{ 1.20 }[/tex]
=> [tex]I = 0.0007 41 \ A[/tex]
help asap
How does the scientist know that the substance goes through a change of state during the time period labeled B on the graph?
a.the temperature remains the same
b.the temperature increases gradually
c.the particles start slowing down
d.the particles start moving faster
Answers
Answer:
The answer is A. The temperature remains the same.
A tennis rackets delivers 500 N on impact with a tennis ball. What is the force of the tennis ball on the racket?
A: this cannot be determined without knowing the mass of the tennis ball
B: the force on the tennis racket is more than 500 N
C: the force on the tennis racket is 500 N
D: the force on the tennis racket is less than 500 N
Answers
Answer:
the a.
Explanation:
because if you compute you can't know the distance
Which best explains why an MRI is useful for diagnosing cancer but ineffective in treating it?
The frequency of the radio waves used is so high that the waves cannot be used to target specific cells.
The wavelength of the radio waves used is so short that the waves cannot be used to target specific cells.
The amount of energy carried by radio waves is enough to provide images but not enough to kill cells.
The amount of energy carried by radio waves is so high that it provides images but can also damage cells.
Answers
Answer:The amount of energy carried by radio waves is enough to provide images but not enough to kill cells.
Explanation:
The reason of MRI should be useful is that the energy amount that should be carried out via the radio waves.
What is Magnetic resonance imaging (MRI) ?It refers to the medical imaging technique that should be applied in the radiology to create the pictures with respect to the anatomy and the process of physiological with related to the body.
Also, it is applied for strong the magnetic field, gradient related to the magnetic field, also the radios waves for produce image in the body organs.
Learn more about wave here: https://brainly.com/question/12734041
A volume of air increases 0.227 m^3 at a net pressure of 2.07 x 10^7 Pa. How much work is done on the air?
Answers
Answer:
The work done on the air is 4.699 x 10⁶ Joules
Explanation:
Given;
increase in air volume, ΔV = 0.227 m³
net pressure of the air, P = 2.07 x 10⁷ Pa
The work done on the air is given by;
W = PΔV
Where;
W is the work done on the air
P is the net pressure
ΔV is the increase in air volume
Substitute the given values and solve for work done;
W = (2.07 x 10⁷ Pa) (0.227 m³)
W = 4.699 x 10⁶ Joules
Therefore, the work done on the air is 4.699 x 10⁶ Joules
Most generation of electricity involves turning turbines to spin coils of metal. However some do not. Give a type of energy that does not involve spinning coils of metal. How does it generate electricity?
Answers
Answer:
Photovoltaic Energy
Explanation:
There are other forms of energy that do not involve spinning of metals to generate electricity, one of many such is the Solar Photovoltaic Energy.
Photovoltaic is a form of energy in which sunlight Is directly into electricity. This type of energy is often used to power devices such as small wrist watches, rechargeable lamps, and others. They are connected together to panels that are joined together in arrays to power people or heavy power plants. Photovoltaic power plants are happening to be one of the fastest growing sources of electricity generation around the world.
The pharyngeal tonsil is found in the __________________________ .
Answers
Answer:
The pharyngeal tonsils are located near the opening of the nasal cavity into the pharynx. When these tonsils become enlarged they may interfere with breathing and are called adenoids.
Rebecca heated 50mL of water from 0 degrees Celsius to 60 degrees Celsius. How much energy did she use to heat the water? Remember: cal=m*deltaT
(WRITE THE WORK!/Give explanation.)
I’ll give BRAINLIEST.
Answers
Answer:
12552 J or 3000 calories
Explanation:
Q = m × c × ∆T
Where;
Q = amount of heat energy (J)
m = mass of water (g)
c = specific heat capacity (4.184 J/g°C)
∆T = change in temperature
For 50mL of water, there are 50g, hence, m = 50g, c = 4.184 J/g°C, initial temperature = 0°C, final temperature = 60°C.
Q = m × c × ∆T
Q = 50 × 4.184 × (60 - 0)
Q = 209.2 × 60
Q = 12552 J
Hence, the amount of heat energy used to heat the water is 12552 J or 3000 calories
an explanation can be consistent but may not be the best explanation for a phenomenon
True
False
Answers
Answer:
true
Explanation:
A basketball is shot with an initial velocity of 16 m/s at an angle of 55° to the
horizontal. What is the approximate horizontal distance that the ball travels in
1.5 s?
Answers
Answer:
approximately 13.77 m
Explanation:
We use the kinematic equations for the horizontal motion which is a uniform non-accelerated motion, and with initial velocity equal to 16 * cos(55). This is described by the equation:
[tex]x=16 * cos(55^o) * t = 9.177 * t[/tex]
then at t = 1.5 seconds, the covered distance becomes:
x = 9.177 * (1.5) = 13.7655 m
Round the answer to the number of decimals that the problem asks.
A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls. At what speed will it's gravitational potential energy (relative to the base of the cliff) be equal to its kinetic energy in m/s?
Answers
Answer:
v = 6.3 m/s
Explanation:
Since no significant air resistance exists, total mechanical energy must be kept constant at any time.At the top of the cliff, all the energy is gravitational potential energy, as follows:[tex]E_{i} = K_{i} + U_{i} = 0 + U_{i} (1)[/tex]
If we choose the ground level as our zero reference level for the gravitational potential energy, Ui is simply:Ui = m*g*h (1)At any height, the sum of the kinetic and the gravitational potential energy must be equal to (1).We know from the question, that at the point of interest, both types of energies must be equal each other, so we can write the following expression from (1):[tex]m*g* h = 2*\frac{1}{2}*m*v^{2} (2)[/tex]
Dividing both sides by m, simplifying, and solving for v, we get:[tex]v = \sqrt{g*h} =\sqrt{9.8m/s2*4.0m} = 6.26 m/s (3)[/tex]
v = 6.3 m/s (with two significative figures)What is energy?
A. A change that appears in an object when forced is applied.
B. The property of a body that gives it mess.
C. The amount of heat produced by the body.
D. The ability of an object to undergo change.
E. The ability of a body to move.
Answers
Answer:
A
Explanation:
Answer: a or e
Explanation:
When the rate of the forward reaction equals the rate of the backward reaction, the system is said to be in
Answers
Answer:
equilibrium
Explanation:
bcoz forward reaction equals backward reaction
if you double the magnitude of a vector, does it follow that the magnitude of the components double? Give example.
Answers
Answer:
The magnitude of the vector clearly doubles if each of its components is doubled.
Explanation:
Consider an underwater spherical air bubble (you can assume the index of refraction of air is 1 and water is 1.33) with radius R. This bubble can act as a lens. What is its focal length?
Answers
Answer:
-2R
Explanation:
The focal length can be calculated using this formula
1/f = (n1/n2-1)(1/r1-1/r2)
1/f = (1/1.33-1)(1/r + 1/r)
= -0.133/1.33(2/R)
F = -2R
The focal length is this
Little Billie has a mass of 25 kg. The acceleration of gravity on the moon is one-sixth of the value on Earth. What is Little Billie's weight on the moon? _____________ What is little Billie's mass on the moon? _____________
Answers
Answer:
Mass is constant everywhere,
But weight is different,
If earth g = 10 then moon's is 1.6666667
Now billie's weight in moon is 41.6667
An engineer is designing a runway for an airport. Of the planes that will use the airport, the
lowest acceleration rate is likely to be 3 m/s2
. The takeoff speed for this plane will be 70 m/s.
Assuming this minimum acceleration, what is the minimum allowed length for the runway?
Answers
Answer:
816m
Explanation:
70^2m/s=2(3m/ss)(x)
x=816
A fish is able to jump vertically out of the water with a speed of 4.45 m/s. What is the speed of the fish as it passes a point 0.6 m above the water?
How much time, after leaving the water does it take for the fish to pass a point 0.6 m above the water while it is on its way down?
Answers
Answer:
Explanation:
given
initial velocity u = 4.45m/s
Height = 0.6m
g = 9.8m/s²
Required
final velocity v
Using the equation of motion;
v² = u²-2gH (upward motion of the fish makes g to be negative)
v² = 4.45²-2(9.8)(0.6)
v² = 19.8025-11.76
v² = 8.0425
v = 2.84 m/s
Hence the speed of the fish as it passes a point 0.6 m above the water is 2.84m/s
To get the time, we will use the formula
v = u - gt
2.84 = 4.45 - 9.8t
2.84-4.45 = -9.8t
-1.61 = -9.8t
t = 1.61/9.8
t = 0.164secs
Hence the time taken is 0.164secs
Select the correct responses to the questions from the drop-down menus. Which type of wave vibrates both side to side and up and down? P waveS wavesurface wave Which type of wave is the first to arrive during an earthquake? P waveS wavesurface wave Which type of wave may make the ground roll? P waveS wavesurface wave
Answers
The S wave vibrates both side to side and up and down whereas P wave is the first to arrive during an earthquake
Seismic waves during earthquake:During the eathquake, two types of seismic waves are generated , P wave and S wave.
The S waves produces vibrations to the ground in a shearing force perpendicular to the direction of propagation of the wave, moving the ground up and down or from side to side. S waves are called secondary waves because arrive after P waves.
The P waves is analogous to longitudinal vibrations, producing vibrations to the ground to compress and expand in the direction of propagation f the wave. They are called primary waves because they are the first type of wave to arrive at seismic recording stations.
Learn more about seismic waves:
https://brainly.com/question/13062627?referrer=searchResults
Answer:
i got it right so chillllll :)
Explanation:
Select the correct responses to the questions from the drop-down menus.
Which type of wave vibrates both side to side and up and down?
✔ S wave
Which type of wave is the first to arrive during an earthquake?
✔ P wave
Which type of wave may make the ground roll?
✔ surface wave
if it took 3.7 seconds for the sound to reach john how far away was the firework shell when it exploded in kilometers assume that the speed of sound in air is 1,236 km/h
Answers
Answer:
1.2703 km
Explanation:
The speed can be calculated using the formula;
Speed (m/s) = distance (m) ÷ time (s)
Based on the information in this question, it took 3.7 seconds for a sound with speed of 1236 km/h to reach John. The distance will be:
Distance = speed × time
However, we need to convert the time in seconds (s) to hour (hr).
1 second = 0.000277778 hour
3.7 seconds = 0.00102778 hours.
Hence,
distance = 1236 × 0.00102778
Distance = 1.2703 km
A rock is thrown with an initial vertical velocity 50 m/s at an angle of 40 degrees.
a. What is the horizontal component of the velocity?
b. What is the vertical component of the velocity?
c. What is the hang timel?
d. What is the peak height?
e. What is the range?
Answers
Answer:
[tex]38.3\ \text{m/s}[/tex]
[tex]32.14\ \text{m/s}[/tex]
6.55 seconds
[tex]52.65\ \text{m}[/tex]
[tex]254.84\ \text{m}[/tex]
Explanation:
u = Initial velocity of rock = 50 m/s
[tex]\theta[/tex] = Angle of throw = [tex]40^{\circ}[/tex]
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
Horizontal component is given by
[tex]u_x=u\cos\theta\\\Rightarrow u_x=50\times \cos40^{\circ}\\\Rightarrow u_x=38.3\ \text{m/s}[/tex]
The horizontal component of the velocity is [tex]38.3\ \text{m/s}[/tex]
Vertical component is given by
[tex]u_y=u\sin\theta\\\Rightarrow u_y=50\times \sin40^{\circ}\\\Rightarrow u_y=32.14\ \text{m/s}[/tex]
The horizontal component of the velocity is [tex]32.14\ \text{m/s}[/tex]
Time of flight is given by
[tex]t=\dfrac{2u\sin\theta}{g}\\\Rightarrow t=\dfrac{2\times 50\sin40^{\circ}}{9.81}\\\Rightarrow t=6.55\ \text{s}[/tex]
The hang time of the rock is 6.55 seconds
Maximum height is given by
[tex]h=\dfrac{u^2\sin^2\theta}{2g}\\\Rightarrow h=\dfrac{50^2\sin^240^{\circ}}{2\times 9.81}\\\Rightarrow h=52.65\ \text{m}[/tex]
Maximum height is [tex]52.65\ \text{m}[/tex]
Range is given by
[tex]d=\dfrac{u^2\sin2\theta}{g}\\\Rightarrow d=\dfrac{50^2\sin(2\times40)^{\circ}}{9.81}\\\Rightarrow d=254.84\ \text{m}[/tex]
The range is [tex]254.84\ \text{m}[/tex]
A 5 kg ball is moving at a velocity of +2 m/s when it
speeds up to +5 m/s in 7 seconds.
Calculate the acceleration.
Answers
Heya!!
For calculate aceleration, lets applicate formula:
[tex]\boxed{a=\frac{V-V_o}{t} }[/tex]
Δ Being Δ
V = Final Velocity = 5 m/s
Vo = Initial Velocity = 2 m/s
a = Aceleration = ? m/s²
t = Time = 7 s
⇒ Let's replace according the formula:
[tex]\boxed{a=\frac{5\ m/s - 2 \ m/s}{7\ s} }[/tex]
⇒ Resolving
[tex]\boxed{ a=0,428\ m/s^{2}}[/tex]
Result:
The aceleration of the object is 0,428 m/s²
Good Luck!!
Answer:
Ksasdasd
Explanation:
7.
As the distance from the Sun increases the time to orbit the Sun
a. Increases
b. Decreases
c. Stays the same
Answers
As the distance from the Sun increases the time to orbit the Sun increases. (a)
Examples:
-- Nearest planet to the sun: Mercury. Time to orbit the sun: 88 days
-- 3rd planet from the sun: Earth. Time to orbit the sun: 1 year
-- 5th planet from the sun: Jupiter. Time to orbit the sun: 12 years
-- 9th closest object to the sun: Pluto. Time to orbit the sun: 248 years
Another pair of examples:
-- Object in a near Earth orbit: International Space Station
Time to orbit the Earth: 90 minutes
-- Object in a far Earth orbit: the Moon
Time to orbit the Earth: 27.3 days
The reason for all of this is: Two things about orbits.
1). The larger the orbit is, the farther the object has to travel around it.
2). The farther out the object is, the slower it travels in its orbit.
This is simply the way gravity works.
Rain drops are formed when water vapor _____.
condenses on grass
evaporates
condenses on dust
freezes
Answers
Answer:
Condenses on dust
Explanation:
Pls brainiest
Answer:
condenses on dust
Explanation:
HELP!!
You are traveling at a speed of 70 miles per hour. How long did it take you to travel 2400 miles?
Answers
Answer:
So do 2400 divided by 70. I got 34.285714 and the numbers behind the decimal are repeating. If you round it you get 34.3
As tall as a tree, as small as a bug, As fast as an eagle, as slow as a slug. Many times in front or behind but never on top, always aligned. What am i
Answers
At what final position would you be if you began at initial position of 4m and drove at 30m/s for 20 seconds?
Answers
Answer:
604m
Explanation:
30 * 20=600
600 + 4 = 604m
Integrated Concepts A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of 1.00×102 MV . (a) What energy was dissipated? (b) What mass of water could be raised from 15ºC to the boiling point and then boiled by this energy? (c) Discuss the damage that could be caused to the tree by the expansion of the boiling steam.
Answers
Answer:
a) 2*10^9 J
b) 764.8 kg
Explanation:
Given that
Energy of charge, q = 20 C
Potential difference, ΔV = 1*10^2 MV = 1*10^2 * 10^6 V = 1*10^8 V
a)
To find the energy dissipated, we use the formula
ΔU = qΔV
ΔU = 20 * 1*10^8
ΔU = 2*10^9 J
b)
Change in temperature, ΔT = 100 - 15°
ΔT = 85° C
Change in energy, ΔU = 2*10^9 J
Specific heat of water, C = 4180 j./Kg.K
Latent heat of vaporization, L(v) = 2.26*10^6 J/Kg
Q1 = mcΔT
Q2 = mL(v)
Net energy needed, U = Q1 + Q2
U = mcΔT + mL(v)
U = m (cΔT + L(v))
m = U /[cΔT + L(v)]
Being that we have all the values, we then substitute
m = 2*10^9 / [(4180 * 85) + 2.26*10^6]
m = 2*10^9 / (3.553*10^5 + 2.26*10^6]
m = 2*10^9 / 2.615*10^6
m = 764.8 kg
c)
Having 765 kg of steam at the temperature would have extreme effect on the tree, damaging it permanently. Possibly even blowing it to pieces
Rebecca heated 50mL of water from 0 degrees Celsius to 60 degrees Celsius. How much energy did she use to heat the water? Remember: cal=m*deltaT
(WRITE THE WORK!/Give explanation.)
Answers
Answer:
Q = 12540 J
Explanation:
It is given that,
Mass of water, m = 50 mL = 50 g
It is heated from 0 degrees Celsius to 60 degrees Celsius.
We need to find the energy required to heat the water. The formula use to find it as follows :
[tex]Q=mc\Delta T[/tex]
Where c is the specific heat of water, c = 4.18 J/g°C
Put all the values,
[tex]Q=50\times 4.18\times (60-0)\\Q=12540\ J[/tex]
So, 12540 J of energy is used to heat the water.
A golf ball starts with a speed of 2 m/s and slows at a constant rate of 0.5 m/s2, what is its velocity after 2 s?
Answers
Answer:
3m/s
Explanation:
Given parameters:
Initial speed = 2m/s
Acceleration = 0.5m/s²
Time = 2s
Unknown:
Final speed = ?
Solution:
To solve this problem, we apply the right motion equation;
V = U + at
V is the final speed
U is the initial speed
a is the acceleration
t is the time
V = 2 + (2 x 0.5)
V = 2 + 1
V = 3m/s