A butterfly is flying around and its velocity(v) as a function of time(t) is given in the graph below where rightwards is the positive velocity direction. What is the butterfly's displacement x from t=2 to 4s? Answer with two significant digits.
Answers
Answer: 19 meters.
Explanation:
We want to find the total displacement between t = 2s and t = 4s.
To do it, we can integrate our function, first write our velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a*t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now we can see that our line passes through the points (1, 0) and (0, -2)
then the slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
and knowing that when t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s^2)*t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
then we have
v(t) = (2m/s^2)*t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2)*(2m/s^2)*t^2 - 2m/s*t + C
where C is a constant of integration, as we are calculating the displacement this constant actually does not matter, so we can use C = 0m
p(t) = (1m/s^2)*t^2 - 2m/s*t for t ≤ 3s
and p(3s) = (1m/s^2)*3s^2 - 2m/s*3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s*t + p(3s) = 4m/s*t + 3m
then the position equation is:
p(t) = (1m/s^2)*t^2 - 2m/s*t ---- t ≤ 3s
p(t) = 4m/s*t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s*4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s^2)*2s^2 - 2m/s*2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
The butterfly displacement x from t=2 to 4s is 19 meters.
What is displacement?The spacing between two specified points is represented by the one-dimensional quantity of displacement (symbolised as d or s), commonly known as length or distance.
The total displacement between t = 2s and t = 4s.
Integrate our function, the velocity equation.
for t ≤ 3s, we have a linear equation, let's write it:
A linear relationship can be written as:
y = a x t + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
The line passes through the points (1, 0) and (0, -2)
The slope is:
a = (0 -(-2)/(1 - 0) = 2/1 = 2
When t = 0s, v(0s) = -2m/s, then our equation is:
v(t) = (2m/s²) x t - 2m/s for t ≤ 3s
now, for t ≥3s the equation is constant, v(t) = 4m/s.
v(t) = (2m/s²) x t - 2m/s -------if t ≤ 3s
v(t) = 4m/s ----- if t ≥ 3s
Now we integrate over time to get the position:
for t ≤ 3s we have:
p(t) = (1/2) x (2m/s²) x t^2 - 2m/s x t + C
where C is a constant of integration, to calculate the displacement this constant actually does not matter,
p(t) = (1m/s²)*t^2 - 2m/s x t for t ≤ 3s
and p(3s) = (1m/s^2) x 3s² - 2m/s x 3s = 9m - 6m = 3m is the initial position of the other part of the function.
for t ≥ 3s we have:
p(t) = 4m/s x t + p(3s) = 4m/s x t + 3m
then the position equation is:
p(t) = (1m/s^2) x t² - 2m/s x t ---- t ≤ 3s
p(t) = 4m/s x t + 3m --- if t ≥ 3s
Now the displacement will be:
p(4s) - p(2s) where for each time, you need to use the correct function:
p(4s) = 4m/s x 4s + 3m = 16m + 3m = 19m
p(2s) = (1m/s²) x 2s²- 2m/s x 2s = 4m - 4m = 0m
p(4s) - p(2s) = 19m - 0m = 19m
Thus, the displacement is 19 m.
To learn more about displacement, refer to the link:
https://brainly.com/question/11934397
#SPJ2
Related Questions
what is tue cause of upthrust ?
Answers
it's caused by a pressure that is large on the button of an object that it is on the top of an object submerged in a liquid.
Explanation:
This is why object appear to weigh less when immersed in a liquid. If the upthrust is greater than the weight of the object, the object will rise up through the liquid.
An object has a kinetic energy of 8.8J, and a mass of 450g. How fast is the object moving?
Answers
Answer:
The formula for KE is
We have everything we need to solve for the velocity, but we first have to convert the mass from grams to kg:
450 g = .450 kg
and we'll rearrange that and solve it for v before we do any math:
so
v = 6.3 m/s rounded to the correct number of sig fig's
A man of mass 75kg stands on a weighing machine in a lift. Determine the reading of the weighing machine when the lift is moving: 1. Upwards with an acceleration of 2m/s² 2. Downwards with a constant velocity of 1.5m/s 3. Downwards with an acceleration of 2.5m/s²
Answers
Explanation:
Given that,
Mass of a man, m = 75 kg
(1) We need to find the reading of the weighing machine when the lift is moving upwards with an acceleration of 2 m/s². When the lift is moving upward, reading of the weighing machine is given by :
R = m(g+a)
R = 75 (9.8+2)
R = 885 N
(2) When the lift is moving downwards with a constant velocity of 1.5m/s. It means that the lift is at rest. So, the reading is :
R = mg
R = 75 (9.8)
R = 735 N
(3) When the lift is moving downwards with an acceleration of 2.5 m/s². In this case,
R = m(g-a)
R = 75 (9.8-2.5)
R = 547.5 N
Hence, this is the required solution.
the moon revolves around the earth in a nearly circular orbit kept by gravitational force exerted by the earth work done will be
Answers
Answer:
Zero because the applied force is perpendicular to the motion of the object.
No work is done on an object moving is a circular path about a central attractive force.
Any work done in such a case would result in a change in the orbit.
The mass of earth 6*10^24kg and radius is 400kg Now find the value of acceleration due to gravity when a object is 3600km from the earth surface
Answers
Answer:
Explanation:
the Earth is 6 xx 10^(24) kg and its radius is 6400 km. Find the acceleration due to gravity on the surface of the Earth. Updated On: 7-4-2021
The fluid inside the hydraulic jack has a pressure of 30,000 Pa. If the surface of
the piston that is used to lift an object is 0.1 m’in area, how much weight can
the jack lift?
Answers
Explanation:
p = F /A
F = P×A
F = 30,000 Pa / 0.1 m²
F = 300,000 N
Explain.
4. State the limitations of our senses to obtain accurate in
formation concerning
our environment.
Answers
Answer:
The limits of our senses are
Limits of Sight
Our vision field of view is 120° sideways and 135° vertically
Angular visual resolution is about an 1/60 of one degree
The presence of blind spots in the eyes
Limits of sound
The hearing range is within 20 - 20,000 Hz and our threshold hearing above 0 to 5 decibel of sound
Limits of taste
We have very limited sense of taste which is partly dependent on our sense of smell with little objectivity in distinguishing tastes
Sense of smell
The establishing of the effectiveness of human sense of smell is gauged on numerous parameters with certain tests being inconsistent, as such, it is difficult to clearly establish the effectiveness of the human sense of smell
In comparison with the sense of smell of other living things such as dogs, the human sense organ is comparatively low
Explanation:
A box with mass of 2 kg is pushed directly horizontally over a horizontal surface (with friction) at a constant speed of 10 m/s. The force of the push is 60 N. How much thermal energy is generated pushing the box a distance of 15 m
Answers
Answer:
E= 600 W
Explanation:
Given that
m = 2 kg
Speed , v= 10 m/s
Force , F= 60 N
Given that box is moving with constant velocity, it means that friction force will be 60 N.
f = 60 N
Therefore total energy generated
E= f x v
E= 60 x 10 = 600 W
E= 600 W
Thus the answer will be 600 W.
what's the difference between force of gravity and the earth's magnetic field?
Answers
Answer:
Gravitational fields are determined only by the mass ( or mass-energy) of a body. ... magnetic fields are produced by charged particles in motion, and depend on the charge and velocity of these particles, but not on their mass. Magnetic fields are 'polar' fields with a North and South polarity.
Explanation:
The moving bicycle moves for sometime even after stopping the paddling.why
Answers
Answer:
when you are paddling the push carry on when you paddle the hard put on the push.
Answer:
Because of inertia
Explanation:
As stated in Newton first law "An object at rest will stay at rest, an object in motion will stay in motion unless it is acted upon by a force."
For an example:
If you have a drink without a lid in a car and a car suddently the car stop, u will automatically try to catch the drink preventing it from spilling. This is because that the drink that was in motion with the car want to stay in motion, but when the car stop, the drink still wanna be in motion, that's why it will be flying off and spill if u don't catch it.
Back to the question:
if a bicyccle is in motion, it will wants to be in motion untill a force act upon it, let's say a bump or fricition.
hope this help. give me the brainliest if u can.
define 1 second time
Answers
Answer:
define 1 second time
One second is the time that elapses during 9,192,631,770 (9.192631770 x 10 9 ) cycles of the radiation produced by the transition between two levels of the cesium 133 atom. ... One second is equal to 1/86,400 of a mean solar day.
Answer:
One part of 86400 part of a day is called one second time.
✌✌✌✌
Will mark as BRAINLIEST......
A balloon is ascending at the rate of 4.9 m/s. A packet is dropped from from the balloon when situated at a height of 100m.
How long does it take the packet to reach the ground ?
What is it's final velocity ?
Answers
Answer:
t = 5.04secsv = -44.49m/sExplanation:
Given parameters
initial velocity u = 4.9m/s
height of drop H = 100m
acceleration due to gravity g = -9.8m/s²(since the body is ascending i.e moving against gravity)
Required
time taken by the packet to reach the ground 't'
Using the equation of motion
S = ut+1/2gt²
0-100 = 4.9t+1/2(-9.8)t²
-100 = 4.9t-1/2(9.8)t²
-100 = 4.9t-4.9t²
4.9t-4.9t² +100 = 0
4.9t²-4.9t² -100 = 0
Multiplying through by 10
49t²-49t-1000 = 0
Using the general equation t = (-b±√b²-4ac)/2a
t = -(-49)±√(-49)²-4(49)(-1000)/2(49)
t = 49±√(2401+196000)/2(49)
t = 49±√(198401)/98
t = 49±√(198401)/98
t = 49±449.42/98
t = (49+449.42)/98
t = 494.42/98
t = 5.04secs
Hence, it took the packet 5.04secs to reach the ground
The final velocity is calculated using the formula v = u + at
v = u-gt
v = 4.9-(9.8)(5.04)
v = 4.9-49.392
v = -44.492m/s
This shows that the final velocity is 44.49m/s(moving downwards)
2. State Newton's third law of motion.
Answers
Answer:
Action and reaction are equal but act in opposite directions
Answer:
Newton’s third law of motion states that “ for every action there is always an equal and opposite reaction.”
Explanation:
If body A exerts a force on body B, then body B will exert an equal and opposite force on body A. It is also called action reaction force. They have equal magnitude but are opposite in direction.
explain radiation and which is the hotest source in the world
Answers
Ramsar has the highest level of natural radiation in the world.
Hot springs located in the Arkaroola Wilderness Sanctuary in Southern Australia are also credited with higher than normal radiation levels, due to spring water coming in contact with rocks rich in uranium and radon.
Distinguish between concave mirror and convex mirror
Answers
Answer:
Concave mirror makes someone looking at it look dwarf or short, while convex mirror stretches the person making the person look weird.
Which statement correctly describes the quantitative relationship between acceleration and net force on an object shown in the data table? (1 point) When the net force applied to an object changes, the mass of the object remains constant. When the net force applied to an object changes, the acceleration changes by a different factor. When the net force applied to an object changes, the mass of the object also changes. When the net force applied to an object changes, the acceleration changes by the same factor.
Answers
Answer:
The correct answer is A
Explanation:
Because when the net force applied to an object changes, the acceleration changes by the same factor. This answer is correct and I hope it helps you too.Hope this helps....
Have a nice day!!!!
The statement that correctly describes the quantitative relationship between acceleration and the net force on an object shown in the data table is as follows:
When the net force applied to an object changes, the acceleration changes by the same factor.Thus, the correct option for this question is D.
What is Acceleration?Acceleration may be defined as a type of rate at which the velocity of an object may change with respect to time. This change in velocity may come in terms of both speed and direction. Acceleration is a type of vector quantity because it has both magnitude and direction.
According to the context of this question, when the net force applied to an object may change, the acceleration may also change. This change is significantly induced by the same factor. This is because the acceleration of an object may directly rely on the net force applied.
Therefore, when the net force applied to an object changes, the acceleration changes by the same factor. Thus, the correct option for this question is D.
To learn more about Acceleration, refer to the link:
https://brainly.com/question/460763
#SPJ2
solve 1 for x if a=-9.8, v=2.7, and t= 35
Answers
Answer:
6097 = x
Explanation:
x = VT + at²/2
x= 2.7 * 35 + 9.8 * (35)²/2
x=6097
Which units represent density? Select all that apply.
Answers
Answer:
D=M/V. That's the formula. Density is expressed, in cubic centimeters.
Explanation:
Answer:g/m³
g/cm³
-kg/L
-kg/cm³
Density in physics, is defined as the mass of the object over its volume. Density is considered as how much matter is contained in a single object by its volume or the matter that it occupies.
D = m / v
Explanation:
A glacier advances at 7.4 x 10^-6 cm/s
How far will it move in 4.2 y?
Answer in units of cm.
cm/s.
Answers
Answer:
236.8 cm
Explanation:
1 yr = 365 days = (365×24×60×60) secs
= 32 × 10^6
distace = velocity × time
= 7.4 × 10^-6 × 32 × 10^6
= 236.8 cm
The glacier will move 976.8 cm when it advances at 7.4 7.4×10⁻⁶ cm/s in 4.2 y
From the question above when we talk about how far, is still the same as distance.
Applying the equation of velocity,
V = d/t................... Equation 1
Where V = velocity, d = distance, t = time
make d the subject of equation 1
d = Vt................ Equation 2
From the question,
Given: V = 7.4×10⁻⁶ cm/s, t = 4.2 year = (4.2×3.154×10⁷) seconds = 1.32×10⁸ seconds
Substitute these values into equation 2
d = (7.4×10⁻⁶)(1.32×10⁸)
d = 9.768×10² cm
d = 976.8 cm
Hence the glacier will advances 976.8 cm
Learn more about distance here: https://brainly.com/question/22491931
Which element has atoms with valence electrons in a higher energy level than those of calcium (Ca)?
(1 point)
oxygen (O)
lithium (Li)
bromine (Br)
cesium (Cs)
Answers
Lithium element contains one electron therefore valence electron will be one.
The highest level of energy is due to valence electrons which are available to the atom.
The calcium has 2 valence electrons which has electrons with high energy.
These energy will be used by the electron during the chemical reaction, and they will either lose or gain valence electron.
Learn more at https://brainly.com/question/24373314
Answer:
calcium
Explanation:
2 electron
(b) A cylinder of cross-sectional area 0.65m2 and
height 0.32m has a mass of 2. Ikg. If there is a
cavity inside, find the volume of the cavity.
(Density of cylinder = 11.053 kg/m^3)
Answers
Answer:
The volume of the cavity is 0.013m^3
Explanation:
To find the volume of the cavity, the major parameter missing is the diameter of the cavity itself. we can obtain this using the following steps:
Step one:
Obtain the volume of the cylinder by dividing the mass of the cylinder by the density.
Volume of the cylinder = 2.1 / 11.053 =0.19[tex]m^{3}[/tex]
Step two:
From the volume of the cylinder, we can get the radius of the cylinder.
[tex]radius = \sqrt{\frac{V}{\pi \times h}} = \sqrt{\frac{0.19}{\pi \times 0.32}} =0.44m[/tex]
Step three:
From the cross-sectional area, we can obtain the radius of the cavity.
Let the radius of the cavity be = r, while the radius of the cylinder be = R
CSA of cavity =
[tex]\pi({R^2}-r^2) = CSA\\0.65 = \pi (0.32^2-r^2)\\r= 0.115m[/tex]
Step Four:
calculate the volume of the cavity using volume =[tex]\pi r^2 \times h[/tex]
Recall that the cavity has the same height as the original cylinder
[tex]volume = \pi \times 0.115^2\times 0.32= 0.013m^3[/tex]
i) A 100 W and 60 W bulb are joined in series and connected to the mains. Which bulb will glow brighter? Why? ii) A 100 W and a 60 W bulb are joined in parallel to the mains. Which bulb will glow brighter? Why?
Answers
Answer:
i) 60 W
ii) 100 W
Explanation:
In each case, the bulb that dissipates the most power is the bulb that glows brighter. Power is voltage times current (P = VI). Using Ohm's law, we can rewrite this as P = I²R or P = V²/R.
Bulbs are rated at a certain power for a certain voltage. P = V²/R, so the bulb with the lower resistance will have the higher power rating. Therefore, the 100 W bulb has a lower resistance than the 60 W bulb.
i) They are in series, so they have the same current. P = I²R, so the bulb with the higher resistance will glow brighter. That's the 60 W bulb.
ii) They are in parallel, so they have the same voltage. P = V²/R, so the bulb with the lower resistance will glow brighter. That's the 100 W bulb.
7. Describe about the difficultites that would arise due to lack of non-uniformity in measurement.
Answers
Answer:
Many difficulties would arise if there was a lack of uniformity in the measurement of various weights and measures between business, industry, individuals and countries. The biggest implications for a lack of uniformity are in health and safety, equity and sustainability.
Explanation:
palike nlng po
a busis moving with the initial velocity 10m/s . after 4 seconds, the velocity becomes 30m/s . find the acceleration produce by bus,......please I need help
Answers
Answer:
5 m/s²
Explanation:
Use the acceleration formula: [tex]a=\frac{v_f-v_i}{t}[/tex]
a = acceleration (m/s²)vf = final velocity (m/s)vi = initial velocity (m/s)t = time (s)Based on the information given to us by the prompt, we know:
vi = 10 m/svf = 30 m/st = 4 sSubstitute these values for the variables to calculate the acceleration:
[tex]a=\frac{30-10}{4}\\\\a=\frac{20}{4}\\\\a=5[/tex]
Therefore, the acceleration of the bus is 5 m/s².
7.
What is TRUE about NIBIN?
ОА. .
It inspired the creation IBIS.
ОВ.
It inspired the creation of IBIS.
O C.
It was created by the FBI and the ATF.
OD.
It was used in the early 1900s.
Reset
Answers
Answer:
the true about n i b i n is they are Commissioner
Answer:
it was created by FBI and ATF
Explanation:
the closes thing I gound to an answer is:
NIBIN is a nationally networked system administered by ATF to assist law enforcement in solving firearms related violent crimes. IBIS is a collection of electronic images ofballistic evidence recovered from crime scenes and test-fired firearms that have been taken into law enforcement custody in the United States.
Will mark as BRAINLIEST....... The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation 4x³+3x²-5x+2 , where x is in meters and t is in sec. a)Find velocity of particle at i) t=2 sec ii) t=4 sec. b) Find the acceleration of the particle at t=3 sec.
Answers
Explanation:
It is given that,
The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation as:
[tex]x=4t^3+3t^2-5t+2[/tex]
Where,
x is in meters and t is in sec
We know that,
Velocity,
[tex]v=\dfrac{dx}{dt}\\\\v=\dfrac{d(4t^3+3t^2-5t+2)}{dt}\\\\v=12t^2+6t-5[/tex]
(a) i. t = 2 s
[tex]v=12(2)^2+6(2)-5=55\ m/s[/tex]
At t = 4 s
[tex]v=12(4)^2+6(4)-5=211\ m/s[/tex]
(b) Acceleration,
[tex]a=\dfrac{dv}{dt}\\\\a=\dfrac{d(12t^2+6t-5)}{dt}\\\\a=24t+6[/tex]
Pu t = 3 s in the above equation
So,
[tex]a=24(3)+6\\\\a=78\ m/s^2[/tex]
Hence, this is the required solution.
If an object floats, the volume of the displaced water is equal to the volume of the whole object. True or false?
Answers
Answer:
True
Explanation:
This is in fact what the Archimedes principle states, and what he used in the famous anecdote about finding if the crown of the King was really made of gold.
You have a reservoir held at a constant temperature of –30°C. You add 400 J of heat to the reservoir. If you have another reservoir at 0°C, how much heat must you add to it so that both reservoirs have the same increase in entropy?
Answers
Answer:
449.38 J
Explanation:
ΔS = ΔQ/T
Where ΔS = entropy change
Q = quantity of heat
T = temperature
First reservoir :
T = –30°C = - 30 + 273 = 243K
Q = 400 J
Second reservoir :
T = 0°C = 273K
Q =?
To have same increase in entropy for both reservoirs :
Q/T of first reservoir = Q/T of second reservoir
400/243 = Q/273
243 * Q = 400 * 273
Q = (400 * 273) / 243
Q = 109,200 / 243
Q = 449.38271
Q = 449.38 J
displacement is the _quantity
Answers
Answer:
vector quantity
I hope it's hepl u
Lyla walks three times per week for 45 minutes at a speed of 4.0 miles per hour. She wants to increase her time what should she do
Answers
Answer:
C. Walk four times per week
Explanation:
If she wants to increase her time then, she has to walk four times per week.
What is speed?The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.
The mathematical expression for speed is given by
speed = total distance /Total time
As given in the problem Lyla walks three times per week for 45 minutes at a speed of 4.0 miles per hour. She must walk four times a week if she wants to extend her time.
Thus, the correct answer is option C.
Learn more about speed from here, refer to the link;
brainly.com/question/7359669
#SPJ2
The question is incomplete, the complete question is,
Lyla walks three times per week for 45 minutes at a speed of 4.0 miles per hour. She wants to increase her time. What should she do?
A. Walk at 4.5 miles per hour.
B. Walk for 50 minutes.
C. Walk four times per week.
D. Walk up and down more hills.