Newton's second equation of motion :-
S=ut+1/2at^2 [where, u is the initial velocity, a is the acceleration and t is the time interval]
This Equation simply finds a relation between distance travelled by a particle (classically) under uniform acceleration.
So let's see what pieces of information (bundles of equations) do we have with us, initially.
We have, a very primary equation with us,
dS/dt = v… (I)
(Considering motion in a straight line only)
And we also have the equation
dv/dt = a…(II)
Simply replacing the v in eqn (II) by eqn (I), we find
d2S/dt^2 = a…(III)
This is what we need to solve. It's easy.
You know,
d2S/dt^2 = d/dt(dS/dt) = a
⟹ dS/dt = ∫adt = at+c1
Since, dS/dt is the velocity of the particle,
Therefore, at t = 0, dS/dt|t = 0 = u
⟹ u = a∗0 + c1 = c1
⟹ c1 = u
Therefore, dS/dt = u + at
Thus, S = ∫(udt + atdt)
⟹ S = ut + 1/2at^2 +c^2
If say, the particle is already having a displacement S0 the moment you start measuring it's motion. Then, at t = 0, S = S0
This makes S = S0 +ut + 1/2at^2
Since, in most of the practical cases, we start measuring a motion when the particle starts displacing (i.e., when S0=0 ),
We get
S = ut + 1/2at^2
Hope it helps :)
ASAP!!! Imagine you are about to purchase a new refrigerator. There are two models that you are considering. Each
refrigerator is required to have an energy efficiency sticker on the door so that the buyer can be aware of the
cost of running the refrigerator. Refrigerator (A) costs $10.00 a month to operate and $700.00 to buy.
Refrigerator (B) costs $15.00 a month to run and $600.00 to buy. Decide which refrigerator you would purchase,
(A or B) and indicate in the answer box why it would be better for the environment
Answer:
model A
Explanation:
model A is more expensive to buy but you pay less per month to run it making it a better purchase in the long run. The cheaper cost of running it is better for the environment due to there being less electricity needed to power it.
"true wisdom is knowing what you don't know"
Reader's Response/explanation
(Y'all I need help)
Answer:
“The only true wisdom is in knowing you know nothing.” ― Socrates. Socrates had it right. Remain humble and appreciate the fact that you don't know everything. ... Thankfully, one's search for knowledge has no end as there is always something new to learn, giving one's life meaning and purpose.
Explanation:
Answer:
knowing wisdom cool
Explanation:
lol
3) A 14 kg object is sitting at the top of a hill that is 100 m high. What is the potential energy of the
object?
Answer:
13,720 joules
Explanation:
Epotential = mgh
mass x gravity x height
Ep= 14 x 9.8 x 100
Ep=13,720 joules
Suppose two objects are gravitationally attracted to each other with some force F. If the mass of object 1 is multiplied by a factor of five and the mass of object 2 is multiplied by a factor of two, what will the new gravitational force be between the objects?
A. F2
B. 1/2F
C. 0.1F
D. 2F/5
E. 5F
J. 10F
Please help will mark brainliest
If F = Gm₁m₂/d², and we change m₁ to 5m₁ and m₂ to 2m₂, then the new magnitude of the gravitational force is
F' = G (5m₁) (2m₂) / d²
F' = 10 Gm₁m₂ / d²
but this is really just F' = 10F. So J is the correct choice.
Hi there!
Using Newton's Law of Universal Gravitation:
[tex]\large\boxed{F_g = G\frac{m_1m_2}{d^2}}[/tex]
Fg = Force of gravity (N)
G = Gravitational Constant
m₁ = mass of object 1 (kg)
m₂ = mass of object 2 (kg)
d = distance between the objects (m)
There is a direct relationship between the masses of the objects and the resulting force of gravity, so we can plug new values in:
[tex]F_g = G\frac{5m_12m_2}{d^2}} = 10G\frac{m_1m_2}{d^2}} = 10F_g[/tex]
Thus, the correct answer is J. 10Fg.
moving east with a constant velocity of 30 m/s for 5 seconds. What is the object's
acceleration?
a. O m/s/s
C. 30 m/s/s
b. 6 m/s/s
d. 150 m/s/s
Find the gravitational force between Earth (5.97 x 1024 kg) and the Sun (1.99 x 1030 kg) knowing they are 1.48 x 1011 m apart.
Using the gravitational force of F= G(m1*m2/r^2)
m1= 5.97 x 10^24 kg (Earth)
m2= 1.99 x 10^30 kg (Sun)
r= 1.48 x 10^11 m
G is a known value, it is 6.672 x 10^-11
All units are proper. Therefore plug in the values and you get 3.16 x 10^22 N.
Let me know if I calculated this wrong and it is something else so I can delete this. Thank you. I don't want to make other students put down the wrong answer.
Answer:
[tex]\boxed {\boxed {\sf F_g \approx 3.62 *10^{22} \ N}}[/tex]
Explanation:
We are asked to find the gravitational force between Earth and the Sun. Use the following formula:
[tex]F_g= \frac{Gm_1m_2}{r^2}[/tex]
G is the universal gravitational constant. One mass (m₁) is the Earth and the other (m₂) is the Sun. r is the distance between the planets.
G= 6.67 * 10⁻¹¹ N*m²/kg²m₁ = 5.97 * 10²⁴ kg m₂= 1.99 * 10³⁰ kg r= 1.48 *10¹¹ mSubstitute the values into the formula.
[tex]F_g = \frac{ (6.67*10^{-11} N*m^2/kg^2)(5.97*10^{24} \ kg)(1.99*10^{30} \ kg) }{ (1.48 *10^{11} \ m)^2}}[/tex]
Multiply the numerator. The units of kilograms cancel.
[tex]F_g = \frac {7.9241601 *10^{44} \ N*m^2}{ (1.48 *10^{11} \ m)^2 }[/tex]
Solve the exponent in the denominator.
[tex]F_g= \frac {7.9241601 *10^{44} \ N*m^2}{ 2.1904*10^{22} \ m^2}[/tex]
Divide. The units of meters squared cancel.
[tex]F_g=3.61767718 *10^{22} \ N[/tex]
The original values all have 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place. The 7 in the thousandth place tells us to round the 1 up to a 2.
[tex]F_g \approx 3.62 *10^{22} \ N[/tex]
The gravitational force between Earth and the Sun is approximately 3.62 *10²² Newtons.
where in space did the expansion of the universe begin?
Answer:
The big bang
Explanation:
It is theorized the expansion of the universe began with the big bang, the universes expansion therefore did not begin in a spot of the universe rather the universe expanded from the big bang.
the federal government sets upper limits for exposure to electromagnetic energy from _____ known as the sar.
The federal government sets upper limits for exposure to electromagnetic energy from telephones known as the SAR.
draw the following vector quantity Using the coordinate system.
a. 190 newton east
b. 120km/hr, 250 north of east
c. 60 meters southwest
The given vectors quantities can be described by their properties of both
magnitude and direction.
a. The drawing of the vector extending from point (0, 0) to (190, 0) on the coordinate plane is attached.b. The velocity vector extending from (0, 0) to (108.76, 50.714) on the coordinate plane is attached.c. The displacement vector extending from (0, 0) to (30·√2, 30·√2) is attached.Reasons:
a. The magnitude of the vector = 190 N
The direction in which the vector acts = East
Therefore, in vector form, we have;
[tex]\vec{F}[/tex] = 190 × cos(0)·i + 190 × sin(0)·j = 190·i
The vector can be represented by an horizontal line, 190 units long
Coordinate points on the vector = (0, 0) and (190, 0)
The drawing of the vector with the above points using MS Excel is attached.
b. Magnitude of the velocity vector = 120 km/hr. 25° North of east
Solution;
The vector form of the velocity is; [tex]\vec{v}[/tex] = 120 × cos(25)·i + 120×sin(25)·j, which gives;
[tex]\vec{v}[/tex] = 120 × cos(25)·i + 120×sin(25)·j ≈ 108.76·i + 50.714·j
[tex]\vec{v}[/tex] ≈ 108.76·i + 50.714·j
Therefore, points that define the vector are; (0, 0) and (108.76, 50.714)
The drawing of the vector is attached
c. The magnitude of the vector = 60 m
The direction of the vector is southwest = West 45° south
The vector form of the displacement is [tex]\vec{d}[/tex] = 60 × cos(45°)·i + 60 × sin(45°)·j
Which gives;
[tex]\vec{d}[/tex] = 30·√2·i + 30·√2·j
Points on the vector are therefore; (0, 0), and (30·√2, 30·√2)
The drawing of the vector is attached
Learn more about vectors here:
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The magnitude of acceleration due to gravity is
Select one:
a. 9.8 m/s
b. 8.9 m/s?
c. 4.6 m/s?
d. 9.8 m/s2
Answer:
The magnitude of acceleration is 9.8 m/s
Explanation:
Its not always in m/s^2 but in m/s due to the unit of distance and time
a galaxy that is a featureless spherical ball of stars would be called a type
Answer:
E0
Explanation:
Yes. The "0" indicates that it is spherical
Drag each tile to the correct location.
Match each process to where it occurs in the carbon cycle.
Ingestion
fossilization
decomposition
combustion
light
energy
oxygen
carbon
dicadde
- sugar
minerak
water
All rights reserved
The order of the location of each process in the carbon cycle are as follows;
Ingestion → Decomposition → Fossilization → CombustionReasons:
Ingestion; During the ingestion process, the products of the direct Sunlight and photosynthesis, which
are energy rich chemical substances are ingested by herbivores.
Decomposition; The plants and animals die and undergo decomposition.
Fossilization; A long period the decomposed plants and animals manifest
into hard petrified materials, with their parts transformed to fossils.
Combustion; The remains of plants and animals, subjected to heat and
pressure due to compression, as when as bacteria decomposition that
removes several other elements, leaving a carbon and hydrogen rich
sludge that can be processed into fuel used for combustion. The
combustion process produces carbon dioxide which restarts the cycle.
Learn more about the carbon cycle here:
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What is the distance traveled by the elevator between 8 s and 24 s?
m
The distance is equal to 6 m traveled by elevator between 8 s and 24 s.
What are distance and displacement?The distance is described as the total length covered by an object. Distance is a scalar parameter with no direction. The distance covered by an object is always +ve, it can never be zero.
The displacement is described as the shortest length between two points by the object. The displacement is a vector parameter with direction & magnitude. The displacement can be +ve, -ve, or zero and can increase or decrease over time.
Given the position of the elevator at time t = 8 s at d = 9 m
The position of the elevator at time t = 24 s at d = 15 m
The distance covered by the elevator = 15 - (9) = 15 - 9 = 6 m
Therefore, the distance traveled by an elevator between 8 s and 24 s is equal to 6 m.
Learn more about distance and displacement, here:
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#SPJ2
An object’s mechanical energy is
a
its energy of motion.
b
the sum of its potential (position) energy and kinetic (motion) energy.
c
the waste energy it produces by friction.
d
not related to the object’s mass.
Explanation:
the sum of its potential (position) energy and kinetic (motion) energy.
how to prove sand is not a fluid even if it takes the shape of a container
A racquetball with a mass of 42 g is moving with a horizontal speed of 7 m/s to the right (+x direction). It hits the wall of the court and rebounds to the hitter with a horizontal speed of 7m/a to the left (-x direction).what is the magnitude of the racquetball's change in momentum?
The magnitude of the racquetball's change in momentum is 0.59 kgm/s approximately.
Given that a racquetball with a mass of 42 g is moving with a horizontal speed of 7 m/s to the right (+x direction).
mass m = 42g = 42/1000 = 0.042kg
initial velocity before collision u = 7 m/s
It hits the wall of the court and rebounds to the hitter with a horizontal speed of 7m/s to the left (-x direction). That is,
velocity after collision v = 7 m/s
To calculate the magnitude of the racquetball's change in momentum, we will use the formula below
Change in momentum = Mv - Mu
Since momentum is a vector quantity, we will consider the direction.
Change in momentum = 0.042 x 7 - ( 0.042 x - 7)
Change in momentum = 0.294 + 0.294
Change in momentum = 0.588 kgm/s
Therefore, the magnitude of the racquetball's change in momentum is 0.59 kgm/s approximately.
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define the unit of work
[tex]\text{The unit of work is same as energy. Newton-meters(Nm) or Joules(J).}\\[/tex]
effect of looping the loop
Answer:
What does this mean? please provide more explanation when asking for help
Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve?
A) v/2
B) v /√ 2
C) 2v
D) v√2
I shall answer it here so this can help other students out
First, FN = mg/cos
On a banked curve, FNx is the only acceleration force
FNx = mv^2/r
FNx = FNsin
mg/cos * sin = mv^2/r
cancel out the mass (m) and sin*1/cos is tan
gtan = v^2/r
rgtan = v^2
√(rgtan) = v (this is the velocity for the smaller radius.)
call larger radius velocity X
for larger radius, it becomes 2r, so √(2rgtan) = X
understand you can do √xy = √x * √y
√(rgtan) * √2 = X (√(rgtan) = v)
v * √2 = X (where X is velocity with larger radius)
Answer:
Answer:
safe speed for the larger radius track u= √2 v
Explanation:
The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.
Also given that r_1= smaller radius
r_2= larger radius curve
r_2= 2r_1..............i
let u be the speed of larger radius curve
now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=
r
1
mv
2
=
r
2
mu
2
................ii
form i and ii we can write
v^2= \frac{1}{2} u^2v
2
=
2
1
u
2
⇒u= √2 v
therefore, safe speed for the larger radius track u= √2 v
What is the energy of a 5 kg object that is held at a height of 3 m above the ground?
Formula
substitute
answer
Answer:
147 Joules
Explanation:
It would be potential energy because it is stored. Potential energy = gravity * mass * height. Gravity is 9.8 m/s² or more specific 9.807 m/s². Potential energy is written in Joules.
9.8 * 5 * 3 = 147 Joules
More specific:
9.807 * 5 * 3 = 147.105 Joules
4) What is the kinetic energy of a 5 kg object moving ot a velocity of 25 m/s?
Help me please I’m confused
N
Select the correct answer.
In which situation is no work considered to be done by a force?
A.
when the angle between the force and displacement is 180°
OB.
when the angle between the force and displacement is 90°
Ос.
when the angle between the force and displacement is 45°
OD.
when the angle between the force and displacement is 0°
on what factors does the quantity of heat of an object depend
Answer:
The quantity of heat given to body depends on: (i) The mass of the body, (ii) The rise (or fall) in the temperature of the body, and (iii) Nature of the material of the body.
Explanation:
Hope this helps
have a great day
~Zero
Say you were at mission control on
Earth. You use radio waves to say "Hello" to an
astronaut on Mars when Mars is 84,000,000
km from Earth. The astronaut hears your "Hello"
280 seconds after you spoke the word. How do
you explain this time lag?
Answer:
because mars is far
Explanation:
so if he shouts louder than he will hear it quicker
write the resistivity of gold, iron ,Mercury, silver,copper? which is bad conductor?
Answer:
Mercury is a bad conductor of heat but a fair conductor of electricity
By the way PURE SILVER is the best conductor of electricity
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-
In the balanced equation, 4KO2 + 2CO2 = 2K2CO3 + 302, which two chem-
icals have a molar ratio of 1:1?
The two chemical compounds having a molar ratio of 1 : 1 is CO₂ and K₂CO₃
4KO₂ + 2CO₂ —> 2K₂CO₃ + 3O₂
4 : 2 : 2 : 3
From the balanced equation above, the coefficients are 4, 2, 2, 3
A careful observation of the equation shows that CO₂ and K₂CO₃ exist in ratio 2 : 2 which can be simplified as 1 : 1
Therefore, we can conclude that CO₂ and K₂CO₃ has molar ratio of 1 : 1
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sue and betti both ski straight down a hill, both starting from rest. sue weighs more than betti. neglecting friction and wind resistance, which skier will be moving the fastest at the bottom of the hill?
Answer:
They are both moving at the same speed since they will have the same acceleration
F = M a describes acceleration
M a = M g sin theta where theta is the slope
One can easily see that
a = g sin theta and the weight does not enter into the equation
The magnitude of acceleration due to gravity is
Select one:
a. 9.8 m/s
b. 8.9 m/s2
c. 4.6 m/s
Answer:
The magnitude of a gravity is always 9.8 which is later approximated to 10m/s.
Answer:
a. 9.8
Explanation:
The magnitude of acceleration due to gravity is 9.8
A car moving at 60 mph slams on its brakes to stop before hitting a deer. Another identical car traveling at 60 mph slows to a stop at a stop sign. Who experiences the greatest impulse during the stop
Happy Holidays!
Recall that:
Impulse = Change in Momentum = mass × change in velocity
Since both cars are identical and have the same initial velocity of 60 mph, them breaking to a stop means that they both experience the same change in velocity.
Thus, both of the cars' impulses are equal.
Va A rail wagon of mass
5000 kg moving at a velocity
of 1.6 ms-1 collides with a
stationary wagon of mass
3000 kg (see Figure 4). After
the collision, the 3000 kg wagon
moves away at a velocity of
1.5 ms-1. Calculate the speed
and direction of the 5000 kg
wagon after the collision.
Answer:
0.7m/s
Explanation:
According to the conservation of linear momentum, the moment before a collision is equal to the moment after the collision. The equation is written as follows: [tex]m_{a}u_{a} + m_{b}u_{b} = m_{a}v_{a} + m_{b}v_{b}[/tex], where [tex]m[/tex] is the mass of the object, [tex]u[/tex] is the initial velocity, and [tex]v[/tex] is the final velocity.
Let's say the object [tex]a[/tex] is our moving wagon and the object [tex]b[/tex] is our stationary wagon. [tex]m_{a} = 500kg, u_{a} = 1.6ms^{-1}[/tex], [tex]m_{b} = 3000kg, u_{b} = 0[/tex], since the wagon is stationary, it doesn't have any initial velocity. After collision, the mass remains the same, but the velocity changes: [tex]v_{a} = ?, v_{b} = 1.5ms^{-1}[/tex]
We can observe that [tex]v_{a}[/tex] is what we're looking for according to the question. Now let's substitute our values.
[tex](5000 * 1.6) + (0) = 5000v_{a} + (3000 * 1.5)[/tex]
[tex]v_{a} = \frac{(5000 * 1.6) - (3000*1.5)}{5000}[/tex] = 0.7m/s