(a) The turtle's initial velocity is 4 m/s, initial position of the turtle is 5 cm, and initial acceleration is -1.25 m/s².
(b) The time when the velocity of the turtle is zero is 3.2 s.
(c) The time taken for the turtle to return to its starting point is 6.4 s.
(d) The time taken for the turtle to travel 30 cm is 0.08 s.
Initial velocity of the turtleThe initial velocity of the turtle is calculated as follows;
[tex]v = \frac{dx}{dt} \\\\x = 5 + 4t -0.625t^2\\\\v(t) = 4 - 1.25t\\\\v(0) = 4-0\\\\v(0) = 4 \ m/s[/tex]
Initial acceleration of the turtleThe initial acceleration of the turtle is calculated as follows;
[tex]a = \frac{dv}{dt} \\\\v(t) = 4 - 1.25t\\\\a = -1.25\ m/s^2[/tex]
Initial position of the turtlex(t) = 5 + 4t - 0.625t²
x(0) = 5 cm
Time when the velocity becomes zerov(t) = 4 - 1.25t
0 = 4 - 1.25t
1.25t = 4
t = 4/1.25
t = 3.2 s
Time taken to return to starting pointThe total distance traveled is calculated as follows
v² = u² + 2ad
0 = (4)² + 2(-1.25)d
0 = 16 - 2.5d
2.5d = 16
d = 16/2.5
d = 6.4 m
Time to travel the given distance;
d = ut + ¹/₂at²
6.4 = (4)t + ¹/₂(-1.25)t²
6.4 = 4t - 0.625t²
0.625t² - 4t + 6.4 = 0
solve the quadratic equation using formula method;
t = 3.2 s
The time travel the distance two times, = 2 x 3.2 s = 6.4 s
Time taken for the turtle to travel 30 cmd = ut + ¹/₂at²
0.3 = (4)t + ¹/₂(-1.25)t²
0.3 = 4t - 0.625t²
0.625t² - 4t + 0.3 = 0
solve the quadratic equation using formula method;
t = 0.08 s
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A potter's wheel is spinning with an initial angular velocity of 11 rad/s . It rotates through an angle of 80.0 rad in the process of coming to rest.
What was the angular acceleration of the wheel?
How long does it take for it to come to rest?
Hi ! I will help you to discuss about Proportionally Changes in Circular Motion. The analogy of proportionally changes in circular motion is same as the analogy of proportionally changes in direct motion. Here you will hear again the terms acceleration and change in speed, only expressed in the form of a certain angle coverage. Before that, in circular motion, it is necessary to know the following conditions:
1 rotation = 2π rad1 rps = 2π rad/s1 rpm = [tex] \sf{\frac{1}{60} \: rps}[/tex] = [tex] \sf{\frac{1}{30}\pi \: rad/s}[/tex] Formula UsedThe following equations apply to proportionally changes circular motion:
Relationship between Angular Acceleration and Change of Angular Velocity[tex] \boxed{\sf{\bold{\omega_t = \omega_0 + \alpha \times t}}}[/tex]
With the following conditions:
[tex]\sf{\omega_t}[/tex] = final angular velocity (rad/s)[tex]\sf{\omega_0}[/tex] = initial angular velocity (rad/s)[tex]\sf{\alpha}[/tex] = angular acceleration (rad/s²)t = interval of the time (s)Relationship between Angular Acceleration and Change of [tex]\sf{\theta}[/tex] (Angle of Rotation)[tex] \boxed{\sf{\bold{\theta = \omega_0 \times t + \frac{1}{2} \times \alpha \times t^2}}}[/tex]
Or
[tex] \boxed{\sf{\bold{(\omega_t)^2= (\omega_0)^2 + 2 \times \alpha \times \theta}}}[/tex]
With the following condition :
[tex]\sf{\theta}[/tex] = change of the sudut (rad)[tex]\sf{\alpha}[/tex] = angular acceleration (rad/s²)t = interval of the time (s)[tex]\sf{\omega_t}[/tex] = final angular velocity (rad/s)[tex]\sf{\omega_0}[/tex] = initial angular velocity (rad/s) Problem SolvingWe know that :
[tex]\sf{\omega_t}[/tex] = final angular velocity = 0 rad/s >> see in the sentence "in the process of coming to rest."[tex]\sf{\omega_0}[/tex] = initial angular velocity = 11 rad/s[tex]\sf{\theta}[/tex] = change of the sudut = 80.0 radWhat was asked :
[tex]\sf{\alpha}[/tex] = angular acceleration = ... rad/s²t = interval of the time = ... sStep by step :
[tex]\sf{\alpha}[/tex] = ... rad/s²[tex] \sf{(\omega_t)^2= (\omega_0)^2 + 2 \times \alpha \times \theta} [/tex]
[tex] \sf{0^2= (11)^2 + 2 \times \alpha \times 80} [/tex]
[tex] \sf{0 = 121 + 160 \alpha} [/tex]
[tex] \sf{-160 \alpha = 121} [/tex]
[tex] \sf{\alpha = \frac{121}{-160}}[/tex]
[tex] \sf{\alpha = -0.75625 \: rad/s^2 \approx \boxed{-0.76 \: rad/s^2}}[/tex]
t = ... s[tex] \sf{\alpha = \frac{\omega_0 - \omega_t}{t}}[/tex]
[tex] \sf{-0.76 = \frac{0 - 11}{t}}[/tex]
[tex] \sf{-0.76t = -11}[/tex]
[tex] \sf{t = \frac{- 11}{-0.76}}[/tex]
[tex] \boxed{\sf{t \approx 14.474 \: s}}[/tex]
ConclusionSo :
The angular acceleration of the wheel approximately -0.76 rad/s² or proportionally as deceleration approximately 0.76 rad/s.It need approximately 14.474 s to come to rest.15C of charge flow through the filament of a light bulb in 22 seconds. What is the strength of the current in the filament?
Answer:
Current(I)= charge(q)/time
I=15/22
I=0.680.68A
Explanation:
Current is flow of charge per unit time. Always make sure the time is in seconds. istthe
What is the effect of the Least Count on the precision/sensitivity of Vernier Callipers?
Answer:
Least count of vernier caliper=.1/50=.002 CM=.02 MM Least count and precision The least count is directly linked with precision. The smaller is the least count number, the more precise the instrument is.
Explanation:
Is a vernier scale accurate or precise? Every instrument has its accuracy defined as the least count of the instrument.As the least count of vernier callipers is 0.01mm,hence it is not accurate beyond the size measurement of 0.01mm.For which it may be called for vernier scale has presize measurement up to 0.01mm.Ans.. What is a vernier caliper?
Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 105 kg·m2. When one person is standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s. However, as this person moves inward to a point located 0.507 m from the center, the angular velocity increases to 0.795 rad/s. What is the person's mass?
For one person standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s, the person's mass is mathematically given as
m = 24.2 kg
What is the person's mass?Generally, the equation for the conservation angular momentum is mathematically given as
(I + m * r0^2) * w0 = (I + m * r^2) * w^2
Therefore
(105 + m * 1.78^2) * 0.517 = (105 + m * 0.524^2) * 0.841
m = 24.2 kg
In conclusion, the mass
m = 24.2 kg
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For the statements based on whether they are described as outcomes of results from thermal energy being added or removed particles move faster particles move slower temperature increases temperature decreases kinetic energy increases kinetic energy decreases thermal energy added thermal energy removed
How does the scintillation detector work?
Answer:
In scintillation detectors the material of the detector is excited to luminescence (emission of visible or near-visible light photons) by the absorbed photons or particles. The number of photons produced is proportional to the energy of the absorbed primary photon. The light pulses are collected by a photo- cathode.
Explanation:
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what’s is the vertical colum of the elements in the periodic table called
it is called groups or families.
Answer:
groups or families
Explanation:
The vertical column of the periodic table are called groups or famileis because of their similar chemical behavior.
the dimensions of a cuboidal block are 2.5 m * 2m * 1.2m its weight 900 n what is the minimum presseure exerted by the block on the surface of its support.?
Answer:
your answer is here 180
Explanation:
900/2.5 * 2 = 180
Answer:
The answer is 180 Pa.
Explanation:
Given;Here, weight = thrust = 900 N,
dimensions are 2.5 m × 2 m × 1.2 m
To Find;Pressure exerted by the block on the surface of its support.Formula;Pressure = Thrust ÷ AreaWe know that, Pressure is inversely proportional to area. For the minimum pressure the area must be more.
So, if the block is resting with 2.5 m × 2 m surface on the support, the pressure will be minimum.
Pressure = 900 N ÷ 2.5 × 2.0 m² = 180 Pa
Thus, The pressure exerted by the block on the support is 180 Pa.
Find the Product or expression of:
(6x+4)2
Answer:
20 or 12
Explanation:
if it is 20 u will have to multiple 6 by 4 and the answer u will multiple it by2 and when it is 12 u will have to add 6 +4 and the answer u will add it to 2
6. When can you say that an object is accelerating?
A. when the speed remains the same
B. When the speed is changing
C. when the instantaneous velocity is the same
D. When there is a uniform motion
give explanation
Answer:
When the speed is changing is the correct answer
Explanation:
Because acceleration is rate of change of velocity
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What is the kinetic energy of a 1375 kg car that travels at 8.5 m/s
Answer:
49671.875
Explanation:
KE = [tex]\frac{1}{2}m[/tex][tex]v^{2}[/tex]
KE = 0.5(1375)(8.5)
= 49671.875 J
The surface of a lake has an area of 15.5 km2. What is the area of the lake in m2?
Answer:
1.55 x 10⁷ m²
Explanation:
Unit conversion
km² → m² 1 km² = 10⁶ m²Solving
15.5 km² = 10⁶ x 15.5 m²155 x 10⁵ m²1.55 x 10⁷ m²If electromagnetic radiation acted like particles in the double-slit experiment, what would be observed? (1 point)
O A series of light and dark bands would appear on the screen.
O Two bright bands would appear on the screen in line with the slits.
O The screen would remain dark because no radiation would reach the screen.
O One bright band would appear in the center of the screen.
If electromagnetic radiation acted like particles in the double-slit experiment, we would observe one bright band would appear in the center of the screen.
Bahavior of particles in double-slit experimentIn a double-slit experiment, single particles, such as photons, pass one at a time through a screen containing two slits.
The photons behave like wave and the constructive interfernce of the waves of these photons will generate a high amplitude wave seen as a bright band in the center of the screen.
Thus, if electromagnetic radiation acted like particles in the double-slit experiment, we would observe one bright band would appear in the center of the screen.
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Which statement about the interference behavior of electromagnetic radiation seen in the double-slit test experiment is true? (1 point)
O Waves that make up the radiation collide with each other so that they add together or cancel each other out.
O Particles that make up the radiation collide with each other so that they add together or cancel each other out.
O Particles that make up the radiation collide with each other and scatter randomly.
O Waves that make up the radiation do not interact with each other.
Waves that make up the radiation collide with each other so that they add together or cancel each other out.
What is Interference?This is the phenomenon which occurs when two waves meet while traveling along the same medium.
In the double-slit test experiment, bright and dark fringes was observed which was caused by the superposition of overlapping light waves originating from the two slits which is why option A was chosen as the most appropriate choice.
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[tex]Question: $x_{1}=\frac{5}{2}[\sin (2 \pi t)+\cos (2 \pi t)], x_{2}=5\left[\sin \left(2 \pi t+\frac{\pi}{4}\right)\right]$[/tex]
Find the ratio of the amplitude of the given motion?
Options:
[tex](a) $\sqrt{2}: 1$\\(b) $2: 1$\\(c) $1: \sqrt{2}$\\(d) $1: 2$[/tex]
Condense x₁ to get
sin(2πt) + cos(2πt) = √2 • (sin(2πt) + cos(2πt))/√2
… = √2 (cos(2πt) cos(π/4) + sin(2πt) sin(π/4))
… = √2 cos(2πt - π/4)
So the amplitude of x₁ is (5/2) • √2 = 5/√2, while the amplitude of x₂ is 5. The ratio between them is then 5/√2 : 5, or equivalently 1/√2 : 1 or 1 : √2.
If the intensity of radiation from an x-ray tube at 2 feet is 100 mR/min, the intensity at a distance of 5 feet will
be?
Answer:
100 mR
Explanation:
list three things that spectra can tell us about objects in space
Answer:
The temperature, the density, and the element of stars.
Explanation:
The spectral line also can tell us about any magnetic field of the star. The width of the line can tell us how fast the material is moving. We can learn about winds in stars from this.
If a→=3i^-2j^-k^ and b→=i^+4j^+k^, find a unit vector n^ normal to the plane containing a→ and b→ such that a→, b→ and n^, in this order, form a right-handed system.
The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
Given data :
The unit vectors
a→=3i^-2j^-k^ and b→=i^+4j^+k^
Determine the unit vector normal to the planeThe unit vector normal to the plane is calculated as
n = [tex]\frac{a*b}{|b*b|}[/tex] ---- ( 1 )
where ; a→ * b→ = 2i - 4j + 14k and |b * b| = [tex]\sqrt{216}[/tex]
back to equation ( 1 )
n = ( 2i - 4j + 14k ) / [tex]\sqrt{216}[/tex]
= [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
Hence we can conclude that The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
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Calculate the power developed by a 68.0 kg athlete who, in 20.0 seconds. runs up stairs that have a vertical height of 8.00 m
Potential energy:-
mgh68(8)(10)680(8)5440JNow
time=t=20sSo
Power:-
PE/t5440/20272WYou ride your bike north for 100 m at a constant speed of 5 m/Your acceleration is…
Answer:
our acceleration is 0 because there is a constant speed..
a = final speed - initial speed / time
final speed = initial speed ( since speed is constant)
therefore acceleration is 0
Which property of matter is conserved in chemical reactions and shown by balanced equations?
O mass
O volume
O density
O shape
Answer:
Mass.
Explanation:
I took the quiz and got the answer right
The sound intensity at a distance of 19 m from a noisy generator is measured to be 0.24 W/m2. What is the sound intensity at a distance of 27 m from the generator
Answer:
0.1111 W/m²
Explanation:
If all other parameters are constant, sound intensity is inversely proportional to the square of the distance of the sound. That is,
I ∝ (1/r²)
I = k/r²
Since k can be the constant of proportionality. k = Ir²
We can write this relation as
I₁ × r₁² = I₂ × r₂²
I₁ = 0.25 W/m²
r₁ = 16 m
I₂ = ?
r₂ = 24 m
0.25 × 16² = I₂ × 24²
I₂ = (0.25 × 16²)/24²
I₂ = 0.1111 W/m²
A DJ is setting up their equipment and measures the sound level near a speaker to be 55.65dB. They decide to add two more speakers next to the first. What would they measure the new sound level to be?
For a DJ is setting up their equipment and measures the sound level near a speaker to be 55.65dB, the new sound level is mathematically given as
L=50.470dB
What would they measure the new sound level to be?Generally, the equation for the sound level is mathematically given as
l=10logl/io
Therefore
logl/io=5.57
Hence
I=3.715*10^−8
In conclusion
L'=10log(3*3.715*10^−8)/10^{-12}
L=50.470dB
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Which point on the graph would have the most kinetic energy?
-Which point on the graph would have the least kinetic energy?
-What point on the graph would have just a little less potential energy than point E?
-What point on the graph would have just a little more potential energy than point F?
-What point on the graph would have just a little less potential energy than point G?
The total mechanical energy is kinetic energy + potential energy, so we can look at the object's potential energy to determine the place where it has maximum and minimum kinetic energy.
Potential energy is determined by the equation PE = mgh, where the height is the only changing variable here. Therefore, we look at the height to answer these questions.
Which point on the graph would have the most kinetic energy?
The point where the object's potential energy is the lowest, aka where its height is the lowest. Point D would have the most kinetic energy.Which point on the graph would have the least kinetic energy?
The point where the object's potential energy is the highest, aka where its height is the highest. Point A would have the least kinetic energy.What point on the graph would have just a little less potential energy than point E?
Look at the point that is just below point E. Point D has just a little less potential energy than point E.What point on the graph would have just a little more potential energy than point F?
Look at the point that is just above point F. Point B has just a little more potential energy than point F.What point on the graph would have just a little less potential energy than point G?
Look at the point that is just below point G. Point B has just a little less potential energy than point E.The diagram shows a heating curve for water.
Which statement best describes what is happening at
segment W-X?
Heating Curve for Water
O Water is absorbing heat.
O Water is releasing heat.
O Aliquid is changing to a gas.
O A gas is changing to a liquid.
z
110
100
90
x
х
Y
80
Temperature (Cº)
70
60
50
40
w
Heat (J)
Answer:
a water is heating up
Explanation:
the water's temperature is inceasing
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A 0.14 kg baseball is dropped from rest. It has a momentum of 0.78 kg.m/s just before it lands on the ground. For what amount of time was the ball in the air?
Answer:
0.568
Explanation:
velocity = -9.8 (t) + Vo
Vo= 0 so v= 9.8(t)
Momentum = mass x velocity
v * 0.14 kg = 0.78 kg m/s
v = 5.571 m/sec
v= 9.8(t) , so substituting v we get , 5.571 = 9.8 * t
t = 5.571/9.8 = 0.568 seconds
The force of a hammer drives a nail into wood. This is an example of. A. An unbalanced force. B. Gravitational force. C. Friction. D. Balanced forces
Answer:
What i got was A. An unbalanced force.
Hope This Helps
A system of four capacitors is connected across a 90-V voltage source as shown in the figure.
(a) What is the potential difference across the plates of the 6.0-µF capacitor? (b) What is the charge on the 2.0-µF capacitor?
For a system of four capacitors is connected across a 90-V voltage source, the potential difference across the plates of the 6.0-µF and 2uF capacitors is mathematically given as
a) vd=30v
b) Q=119.7uc
What is the potential difference across the plates of the 6.0-µF and 2uF capacitors?Generally, the equation for the charge across 6uf is mathematically given as
Q=C6Vd
Where
1/c36=1/3+1/6
c36=2
Q3=2*90
Q3=180
Therefore
vd=180/6
vd=30v
In conclusion
1/c24=1/2+1/4
C24=1.33uf
Q2=1.33*90
Q=119.7uc
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What is the cycle of a breaststroke?
Answer:
Breaststroke can be divided up into 4 distinct phases, which consists of the out sweep, in sweep, breathing phase, and lunge, extension, or recovery phase.
Explanation:
pa follow po
A 3 Hz wave has a wavelength of 0.4 m. Calculate the speed of the wave (in m/s).
The speed of the wave with the given frequency and wavelength is 1.2m/s.
Given the data in the question;
Wavelength of the wave; [tex]\lambda = 0.4m[/tex]Frequency; [tex]f = 3Hz = 3s^{-1}[/tex]Speed of the wave; [tex]v = \ ?[/tex]WavelengthWavelength is the distance over which the shapes of waves are repeated. It is the spatial period of a periodic wave.
It is expressed as;
[tex]\lambda = \frac{v}{f}[/tex]
Where v is velocity/speed and f is frequency.
Now, we can easily get the speed of the wave by substituting our given values into the expression above.
[tex]\lambda = \frac{v}{f} \\\\0.4m = \frac{v}{3s^{-1}}\\ \\v = 0.4m * 3s^{-1}\\\\v = 1.2ms^{-1}\\\\v = 1.2m/s[/tex]
Therefore, the speed of the wave with the given frequency and wavelength is 1.2m/s.
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