The radial acceleration of a body a distance R from the center of a circular path and with period T has magnitude a such that
a = 4 π ² R / T ²
The given period is
T = 365.3 days ≈ 3.156 x 10⁷ s
(i.e. multiply the number of days by 24 hours/day and 3600 seconds/hour)
So the Earth's radial acceleration is
a = 4 π ² (1.5 x 10¹¹ m) / (3.156 x 10⁷ s)²
a ≈ 0.0059 m/s²
If the total mechanical energy of the block spring system is 512 J, what is the amplitude for this oscillation?
Answer:
A = 2.26 m
Explanation:
Given that,
The total mechanical energy of the block spring system is 512 J
Let the spring constant, k = 200 N/m
We need to find the amplitude for this oscillation. The mechanical energy of the spring mass system is given by :
[tex]E=\dfrac{1}{2}kA^2[/tex]
k is spring constant
[tex]A=\sqrt{\dfrac{2E}{k}} \\\\A=\sqrt{\dfrac{2\times 512}{200}} \\A=2.26\ m[/tex]
So, the amplitude of the oscillation is 2.26 m
Sitting in a parked bu s, you suddenly look up at a bus moving alongside and it appears that you are moving. Why is this? How about with both buses moving in opposite directions?
Answer:
Explained below
Explanation:
When one sits in a parked bus, and another bus is moving alongside, it means the other bus is moving relative to you. However, this makes the brain register in such a way that it's feels the bus you are in is the one moving.
In the second case where both buses are moving in opposite directions, the brain will register it in such a way that it seems the bus in which you are at is moving at a far higher speed than the speed in which it is actually moving.
This is because the relative velocity of the other vehicle is higher and it is therefore what makes your brain think your bus is moving at a faster speed.
What is energy ? Use in your own words.
Answer:
the potential for causing changes
Explanation:
Erma built the simple motor shown below with a battery, a permanent magnet, a copper coil of wire, and an iron bar. When the motor is turned on, the iron bar and coil spin in a circle The motor transforms _______ energy into _______ energy. Question 27 options: mechanical; chemical electrical; mechanical mechanical; electrical thermal; electrical
Answer:
electrical to mechanical
Explanation:
Why is the metric system used globally, but we use the US customary units?
Answer:
The biggest reasons the U.S. hasn't adopted the metric system are simply time and money. When the Industrial Revolution began in the country, expensive manufacturing plants became a main source of American jobs and consumer products.
Explanation:
A baseball player exerts a force of 100 N on a ball for a distance of 0.5 mas he throws it. If the ball has a mass of 0.15 kg, what is its velocity as it leaves his hand?
Answer:
25.82 m/s
Explanation:
We are given;
Force exerted by baseball player; F = 100 N
Distance covered by ball; d = 0.5 m
Mass of ball; m = 0.15 kg
Now, to get the velocity at which the ball leaves his hand, we will equate the work done to the kinetic energy.
We should note that work done is a measure of the energy exerted by the baseball player.
Thus;
F × d = ½mv²
100 × 0.5 = ½ × 0.15 × v²
v² = (2 × 100 × 0.5)/0.15
v² = 666.67
v = √666.67
v = 25.82 m/s
This question involves the concepts of the law of conservation of energy and kinetic energy.
The baseball leaves the hand with a velocity of "25.82 m/s".
From the law of conservation of energy the work done on the ball must be equal to the kinetic energy of the ball:
[tex]W=K.E\\\\Fd=\frac{1}{2}mv^2\\\\v=\sqrt{\frac{2Fd}{m}}\\\\v=\sqrt{\frac{2(100\ N)(0.5\ m)}{0.15\ kg}}[/tex]
where,
F = force applied = 100 N
d = displacement of ball = 0.5 m
m = mass of ball = 0.15 kg
v = 25.82 m/s
Learn more about the law of conservation of energy here:
brainly.com/question/20971995?referrer=searchResults
The attached picture explains the law of conservation of energy.
You are designing a flywheel. It is to start from rest and then rotate with a constant angular acceleration of 0.200 rev/s^2. The design specifications call for it to have a rotational kinetic energy of 330 J after it has turned through 30.0 revolutions.
What should be the moment of inertia of the flywheel about its rotation axis?
Express your answer with the appropriate units.
Answer: 1.14 kg*m/s
Explanation:
The first person explained everything right, they just forgot to convert the angular acceleration to rads/sec^2 from revs/sec^2. Once that is converted, your answer should come out right.
Another small thing, the answer there has an extra unnecessary step. It tells you to find the square root of w^2 to find w but that is unnecessary since the final equation asked for w^2. Hope this helps! :)
The moment of inertia I of the flywheel about its rotation axis is
[tex]1.39Kgm^2[/tex]Given
Angular displacement,
[tex]\theta = 30rev \\\\\theta = (30) * 2\pi rad \\\\\theta = 188.495rad[/tex]
Therefore, Final angular velocity (w) will be:
[tex]w^2 = 2\alpha\theta\\\\w^2 = 2 * (0.200 * 2\pi) * (188.49)\\\\w^2 = 473.73\\\\w = 21.76 rad/s[/tex]
Therefore,
moment of inertia
[tex]I = 2 * K / w^2[/tex]
[tex]I = 2 * 330 / 473.73[/tex]
[tex]I = 1.39kgm^2[/tex]
For more information on moment of inertia
https://brainly.com/question/19557854?referrer=searchResults
someone help please
waves disturb ____, but do not transmit it.
a. energy
b. matter
c. sound
d. none of the above
Answer:
b. matter
Explanation:
Waves disturb matter but do not transmit it.
Waves are disturbances that transmit energy from one point to another. Although they cause disturbances, they do not transfer the matters in the medium.
Energy is propagated by a wave. When for example, sound waves are produced, the disturbance is propagated via particle - particle interaction But after the wave train moves, the particles remain.A rollercoaster moves from the bottom of a hill and approaches the top of the hill. If friction between the wheels and the track is ignored, which statement describes the components of the total energy?
*answer choices pic attached*
{If anyone has the answers to the Energy Flows Quick Check or others please let me know}.
Answer:
The kinetic energy remains same and gravitational potential energy increases.
Explanation:
KINETIC ENERGY:
As, we know that the kinetic energy depends upon the speed of the object. Hence, the kinetic energy is given as:
K.E = (1/2)mv²
where,
m = mass
v = speed
K.E = Kinetic Energy
Since, the friction is ignored, therefore the speed of roller coaster will remain same.
Therefore, its Kinetic Energy will also remain same.
POTENTIAL ENERGY:
The potetial energy od a body depends upon its height, as follows:
P.E = mgh
where,
P.E = potential Energy
m = mass
g = acceleration due to gravity
h = height
As, the roller coaster moves up hill its height increases.
Therefore, its potential energy will also increase.
hence, the correct option is:
The kinetic energy remains same and gravitational potential energy increases.
When is a magnetic force produced in a copper wire?
O A. Whenever the wire is connected to a magnet
B. Whenever the wire is wrapped around an iron bar
C. Whenever there is current in the wire
D. Whenever the wire is coiled
Answer:
ur answer is d
Explanation:
it has to be coiled to give off magnetic energy
Light from two lasers is incident on an opaque barrier with a single slit of width 4.0 x 10-5 m. One laser emits light of wavelength 4.0 x 10-7 m and the other is 6.0 x 10-7 m. A screen to view the light intensity pattern is 2.0 m behind the barrier. What is the distance from the center of the pattern to the nearest completely dark spot (dark for both colors)?
Answer:
y = 6 10⁻² m
Explanation:
This is a diffraction exercise which is described by the expression
a sin θ = m λ
we can use trigonometry to find the distance from the inside of the screen to the dark point (y)
tan θ = y / L
angles are very small in diffraction experiments, so we can approximate
tan θ = sin θ /cos θ = sin θ
sin θ = y / L
substituting
a (y / L) = m λ
Let's find the points where the intensity becomes zero
y = m L λ / a
λ₁ = 4.0 10⁻⁷ m
m = 1
y = 1 2.0 4.0 10⁻⁷/ 4.0 10⁻⁵
y = 2 10⁻² m
m = 2
y = 4 10⁻² m
λ₂ = 6.0 10⁻⁷ m
m = 1
y = 1 2.0 6.0 10⁻⁷ / 4.0 10⁻⁵
y = 3 10⁻² m
m = 2
y = 6 10⁻² m
if we want a point where the two colors are dark, we set the two expressions equal
y₁ = y₂
m₁ L λ₁ / a = m₂ L λ₂ / a
m₁/m₂ = λ₂/λ₁
m₁ / m₂ = 6 10⁻⁷ / 4 10⁻⁷
m₁ / m₂ = 1.5
since the quantities m must be integers, the smallest relation that the relation fulfills is
m₁ = 3
m₂ = 2
the distance for this destructive interference is
y = 3 2 4.0 10⁻⁷ / 4.0 10⁻⁵
y = 6 10⁻² m
this is the first point where the minimum of the two wavelengths coincide
The current theory of the structure of the Earth, called plate tectonics, tells us that the continents are in constant motion.
Assume that the North American continent can be represented by a slab of rock 4450 km on a side and 31 km deep and that the rock has an average mass density of 2620 kg/m3.
The continent is moving at the rate of about 1 cm/year.
What is the mass of the continent? Answer in units of kg.
(part 2 of 3)
What is the kinetic energy of the continent? Answer in units of J.
(part 3 of 3)
A jogger (of mass 77 kg) has the same kinetic energy as that of the continent.
What would his speed be? Answer in units of m/s.
Answer:
1) The mass of the continent is approximately [tex]1.608\times 10^{21}[/tex] kilograms.
2) The kinetic energy of the continent is approximately [tex]8.04\times 10^{16}[/tex] joules.
3) The speed of the 77 kg-jogger would be approximately [tex]45.698\times 10^{6}[/tex] meters per second.
Explanation:
1) The mass of the North American continent can be estimated by using the following formula under the assumption that rock has an uniform density:
[tex]m = \rho \cdot L^{2}\cdot h[/tex] (1)
Where:
[tex]m[/tex] - Mass of the continent, measured in kilograms.
[tex]\rho[/tex] - Average density of the rock, measured in kilograms per cubic meter.
[tex]L[/tex] - Side of the continent, measured in meters.
[tex]h[/tex] - Depth of the continent, measured in meters.
If we know that [tex]\rho = 2620\,\frac{kg}{m^{3}}[/tex], [tex]L = 4.450\times 10^{6}\,m[/tex] and [tex]h = 31\times 10^{3}\,m[/tex], then the mass of the continent is:
[tex]m = \left(2620\,\frac{kg}{m^{3}} \right)\cdot (4.450\times 10^{6}\,m)^{2}\cdot (31\times 10^{3}\,m)[/tex]
[tex]m = 1.608\times 10^{21}\,kg[/tex]
The mass of the continent is approximately [tex]1.608\times 10^{21}[/tex] kilograms.
2) By assuming that continent can be represented as a particle, we define its kinetic energy as:
[tex]K = \frac{1}{2}\cdot m \cdot v^{2}[/tex] (2)
Where:
[tex]K[/tex] - Translational kinetic energy, measured in joules.
[tex]v[/tex] - Motion rate of the continent, measured in meters per second.
If we know that [tex]m = 1.608\times 10^{21}\,kg[/tex] and [tex]v = 1\times 10^{-2}\,\frac{m}{s}[/tex], then the kinetic energy of the continent is:
[tex]K = \frac{1}{2}\cdot (1.608\times 10^{21}\,kg)\cdot \left(1\times 10^{-2}\,\frac{m}{s} \right)^{2}[/tex]
[tex]K = 8.04\times 10^{16}\,J[/tex]
The kinetic energy of the continent is approximately [tex]8.04\times 10^{16}[/tex] joules.
3) The speed of the jogger is derived from the definition of translational kinetic energy:
[tex]v = \sqrt{\frac{2\cdot K}{m} }[/tex]
If we know that [tex]K = 8.04\times 10^{16}\,J[/tex] and [tex]m = 77\,kg[/tex], then the expected speed of the jogger is:
[tex]v = \sqrt{\frac{2\cdot (8.04\times 10^{16}\,J)}{77\,kg} }[/tex]
[tex]v\approx 45.698\times 10^{6}\,\frac{m}{s}[/tex]
The speed of the 77 kg-jogger would be approximately [tex]45.698\times 10^{6}[/tex] meters per second.
An object with a mass of 3.0 kg has a
force of 9.0 newtons applied to it. What
is the resulting acceleration of the
object?
[tex] \LARGE{ \underline{ \tt{Required \: answer:}}}[/tex]
We have:
Mass of the object = 3 kgForce on the object = 9 NWe need to find:
Resulting accleration of the object?Solution:
According to Newton's 2nd law of motion, or quantitative measure of Force:
Force = Mass × AcclerationUsing this,
➝ F = ma
➝ 9N = 3 kg × a
➝ a = 9/3 m/s²
➝ a = 3 m/s²
Hence,
The resulting accleration of the object is 3 m/s². And we are done! :D⛱️ [tex] \large{ \blue{ \bf{FadedElla}}}[/tex]
An ant crawled from a hole to the food. For the first 6 minutes,it travelled at an average speed of 15m/min. For The next 9 minutes it travelles at an average speed of 10m/min what was the average speed of the whole journey?
Answer:
v = 12 m/min
Explanation:
By definition, the average velocity is the rate of change of the position with respect to time, as follows:[tex]v_{avg} =\frac{x_{f} -x_{o} }{t_{f}-t_{o} } (1)[/tex]
Choosing x₀ = 0 and t₀ =0, (1) reduces to :[tex]v_{avg} = \frac{x_{f} }{t_{f} } (2)[/tex]
From the givens, we have:tif = 6 min + 9 min = 15 min
In order to get xf, we know that during the first part, vavg = 15 m/min, so solving for xf:[tex]x_{f1} = v_{avg1}* t_{1} = 15 m/min * 6 min = 90 m (3)[/tex]
For the following 9 min, we know that the average speed was 10m/min, so the distance traveled during the second part of the trip was simply:[tex]x_{f2} = v_{avg2} *t_{2} = 10m/min * 9 min = 90 m (4)[/tex]
Adding (3) and (4):[tex]x_{f} = 90 m + 90 m = 180 m (5)[/tex]
Replacing xf and tif in (2), we finally get:[tex]v_{avg} =\frac{x_{f} }{t_{f}} =\frac{180m}{15 min} = 12 m/min (6)[/tex]
An explanation of the relationships among particular phenomena.
Answer:
Theory
Explanation:
Theory is a term that is used often in academic work or scientific research to explain certain things or conditions established on universal principles or laws.
It is used to describe the "why and how" or the reason behind the occurrence of a situation.
Hence, it is correct to conclude that THEORY is "an explanation of the relationships among particular phenomena."
Answer:
E) Theory
Explanation:
Edge 2020
Brainliest?
A projectile is shot straight up from the earth's surface at a speed of 11,000 km/hr. How high does it go? ________km?
Taken from "Physics for Scientists and Engineers by Randall D. Knight 2nd Edition. Chapter 13 #34. There is an answer in the database already, but I do not understand it.
Answer:
476.35 km
Explanation:
The following data were obtained from the question:
Initial velocity (u) = 11000 km/hr
Final velocity (v) = 0 km/hr (at maximum height)
Acceleration due to gravity (g) = 9.8 m/s²
Maximum height (h) = ?
Next, we shall convert 9.8 m/s² to km/hr². This is illustrated below:
1 m/s² = 12960 km/hr²
Therefore,
9.8 m/s² = 9.8 m/s² × 12960 km/hr² / 1 m/s²
9.8 m/s² = 127008 km/hr²
Thus, 9.8 m/s² is equivalent to 127008 km/h²
Finally, we shall determine the maximum height reached by the projectile.
This is illustrated below:
Initial velocity (u) = 11000 km/hr
Final velocity (v) = 0 km/hr (at maximum height)
Acceleration due to gravity (g) = 127008 km/hr²
Maximum height (h) = ?
v² = u² – 2gh (since the projectile is going against gravity)
0² = 11000² – (2 × 127008 × h)
0 = 121×10⁶ – 254016h
Collect like terms
0 – 121×10⁶ = – 254016h
– 121×10⁶ = – 254016h
Divide both side by – 254016
h = – 121×10⁶ / – 254016
h = 476.35 km
Thus, the maximum height reached by the projectile is 476.35 km
it is the question 12 part okay
Answer:
Yeah it's ok I think. Also, I can't see the answer you gave so maybe updating the question would be nice.
200. Un automóvil se desplaza
hacia la izquierda con
velocidad constante v,
en el momento en que se
deja caer un saco de lastre
desde un globo en reposo.
El vector que representa
la velocidad del saco vista
desde el automóvil en ese
instante en que se suelta es
Explain what it means when we say a substance is magnetic.
Discuss the relationship between electric and magnetic fields.
Which types of wires (cooper, aluminum, or string) are ferromagnetic metals?
Answer: See the explanation.
Explanation:
When we say a substance is magnetic it means the atoms are lined in a way that created a magnetic field that goes from one side to the other
These are essentially two aspects of the same thing, because a changing electric field creates a magnetic field, and a changing magnetic field creates an electric field. This is the relationship.
Answer: Copper isn't ferromagnetic,
Aluminum isn't ferromagnetic,
String does have a ferromagnetic property
Dolphins rely on echolocation to be able to survive in the ocean. In a 20 °C ocean, a dolphin produces an ultrasonic sound with a frequency of 125 kHz. What is the wavelength of this sound, in meters?While remaining stationary, the dolphin emits a sound pulse and receives an echo after 0.220 s. How far away, in meters, is the reflecting object from the dolphin?
Answer:
wavelength = 0.01 m
distance = 162.8 m
Explanation:
Given that;
Speed of sound in water = 1,480 meters per second
Frequency of ultrasound = 125KHZ
From=
v=λf
v= speed of sound
λ= wavelength of sound
f= frequency of sound
λ= 1,480 ms-1/125 * 10^3 Hz
λ= 0.01 m
From
v = 2x/t
where;
v= velocity of sound in water
x= distance traveled
t = time taken
x = vt/2
x = 1,480 ms-1 * 0.220 s/2
x= 162.8 m
PLEASE HELP!!
Which statement accurately describes a balanced force?
A 2-N force presses down on the marble at the same time as a 1.5-N force presses up on the marble.
A marble rolling downhill suddenly comes to rest at a garden wall.
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
A marble resting on the sidewalk suddenly begins to roll downhill without being touched.
Answer:
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
Explanation:
just took test
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Balanced force is when the net force applied on the object is zero than said to be balanced.
A 25-N force acts on the left side of the marble at the same time as a 25-N force acts on the right side of the marble.
To learn more about force refer to the link:
brainly.com/question/13191643
#SPJ2
A pulley is in the form of a uniform solid cylinder of radius 7cm and mass 2kg. One end of a very light rope is fixed to wind the pulley and the other end is
free. When we pull the free end of the rope the pulley starts rotating from rest and accelerates uniformly. If the angular acceleration is 100rad/s2 so the
constant force that we exert on the pulley through the rope is:
Chọn một:
a.
200 N
b.
7N
C
0.49 N
d.
49 N
Answer:
correct is b 7N
Explanation:
The torque is
Στ = I α
torque
τ = F x R
bold, indicate vectors. The magnitude of torque is
τ = F R sin θ
in this case the angle is 90º so sin 90 = 1
τ = F R
The moment of inertia of a cylinder
I = ½ M R²
substitute
F R = ½ M R² α
F = ½ M R α
reduce to the SI system
R = 7 cm (1m / 100cm) = 0.07 m
calculate
F = ½ 2 0.07 100
F = 7 N
Consider a block sliding down a ramp whose motion is opposed by frictional forces. The total energy of this system is modeled by the equation:
Etotal = 1/2mv^2 + mgh + Ff(f is underscore)d
Which part of the equation represents the amount of energy converted to thermal energy?
A. mg
B. Ffd
C. mgh
D. 1/2 mv^2
Answer:
Energy Flows Quick check answers:
1. Ffd.
2. The kinetic energy decreases, and gravitational potential energy increases.
3. The internal energy of the system increases.
4. KEbox= Etotal-mgh
5. Etotal = 1/2m1(v1)^2+1/2m^2(v2)^2+U
The part of the equation that represents the amount of energy converted to thermal energy is [tex]F_f d[/tex].
The given equation for the total energy of a system;
[tex]E_{total} = \frac{1}{2} mv^2 \ +\ mgh\ + \ \ F_fd[/tex]
The definition of the various terms in the energy equation is given as;
[tex]E_{total}[/tex]: this is the total mechanical energy of the system[tex]\frac{1}{2} mv^2[/tex]: this is the kinetic energy of the system[tex]mgh[/tex]: this is the potential energy of the system[tex]F_f d[/tex]: this is the energy lost due to friction.The energy lost due to friction is equal to the energy converted to thermal energy.
Thus, the part of the equation that represents the amount of energy converted to thermal energy is [tex]F_f d[/tex].
Learn more here:https://brainly.com/question/17858145
When the palmaris longus muscle in the forearm is flexed, the wrist moves back and forth. If the muscle generates a force of 39.5 N39.5 N and it is acting with an effective lever arm of 2.75 cm2.75 cm, what is the torque that the muscle produces on the wrist?
Answer:
Explanation:
Torque is expressed according to the formula;
Torque = Force × radius
Given
Force = 39.5N
Radius = 2.75cm
Convert radius to metres
100cm ,= 1m
2.75cm = (2.75/100)
2.75cm = 0.0275m
Find the torque
Torque = 39.5×0.0275
Torque = 1.08625Nm
Hence the torque is 1.08625Nm
Temporary Wind Turbines-
Answer:
lol what
Explanation:
An oscilloscope is set on a TIME/DIV setting of 50 ms. There are 10 divisions on the time scale. A sinewave on the oscilloscope display has exactly three full cycles of the sine wave that fit on the 10 divisions. What is the frequency of the wave?
Answer:
f= 6 Hz
Explanation:
Since the TIME/DIV setting is set to 50 ms, and there 10 divisions on the time scale, that means that full scale display is 500 msec.If a sinewave has exactly three full cycles of the sine wave that fit on the 10 div, this means that one cycle is just one-third of the 10 div value, as follows:[tex]T = \frac{500 msec}{3} = 166.7 msec (1)[/tex]
Since the frequency of a wave is just the number of cycles per unit time, can be written as follows:F = 1/T = 1/(166.7 msec) = 6 HzThe sun is 150,000,000 km from earth; its diameter is 1,400,000 km. A student uses a 4.6-cm-diameter lens with f = 10 cm to cast an image of the sun on a piece of paper. What is the diameter of the image on the paper?
Answer:
Explanation:
the image distance can be calculated using below formula of lens
1/v=1/- 1/u
Where
u= Object distance = 15×10^7km
Diameter = 1400000 km
Diameter of lens = 4.6 cm
f= Focal length ( 10 cm)= 1×10^-4
We can substitute to the above formula we have
1/15×10^7km+1/1×10^-4
V=0.001km
Therefore, paper stayed on the focus, hence the sharp image
what happens to the strength of an electromagnet when the voltage in the coils of the solenoid is decreased
Answer:
Make sure you look at the wording!
Explanation:
if the last word is increased, the answer is increased
if the last word is decreased, the answer is it decreases!
An object moves in along the x-axis with an acceleration given by: a = 5t (m/s2). The position of the object at t=0.0 is 6 m, and its velocity at t=0.0 s is 4 m/s. Calculate the position at t=5 s.
Answer:
The position of the object at [tex]t = 5\,s[/tex] is 130.167 meters.
Explanation:
Let [tex]a(t) = 5\cdot t\,\left[\frac{m}{s^{2}} \right][/tex] the acceleration experimented by the object along the x-axis. We obtain the equation for the position of the object by integrating in acceleration formula twice:
Velocity
[tex]v(t) = \int {a(t)} \, dt[/tex] (1)
[tex]v(t) = 5\int {t} \, dt[/tex]
[tex]v(t) = \frac{5}{2}\cdot t^{2}+v_{o}[/tex] (2)
Where [tex]v_{o}[/tex] is the initial velocity of the object, measured in meters per second.
Position
[tex]s(t) = \int {v(t)} \, dt[/tex] (3)
[tex]s(t) = \frac{5}{2}\int {t^{2}} \, dt+v_{o}\int \, dt[/tex]
[tex]s(t) = \frac{5}{6}\cdot t^{3}+v_{o}\cdot t + s_{o}[/tex] (4)
Where [tex]s_{o}[/tex] is the initial position of the object, measured in meters per second.
If we know that [tex]s_{o} = 6\,m[/tex], [tex]v_{o} = 4\,\frac{m}{s}[/tex] and [tex]t = 5\,s[/tex], then the position of the object is:
[tex]s(5) = \frac{5}{6}\cdot (5)^{3}+\left(4\right)\cdot (5)+6[/tex]
[tex]s(5) = 130.167\,m[/tex]
The position of the object at [tex]t = 5\,s[/tex] is 130.167 meters.
A cyclist is riding his bike up a mountain trail. When he starts up the trail, he is going 8 m/s. As the trail gets steeper, he slows to 3 m/s in 1 minute. What is the cyclist’s acceleration?
Answer:
[tex]\boxed {\boxed {\sf a\approx -0.08 \ m/s^2}}[/tex]
Explanation:
Acceleration can be found by dividing the change in velocity by the time.
[tex]a=\frac{v_f-v_i}{t}[/tex]
The final velocity is 3 meters per second. The initial velocity is 8 meters per second.
We need to convert the time to seconds.
t= 1 minute 60 seconds = 1 minute t=60 secondsSo, we know that:
[tex]v_f=3 \ m/s \\v_i= 8 \ m/s\\t= 60 \ s[/tex]
Substitute the values into the formula.
[tex]a=\frac{3 \ m/s - 8 \ m/s}{60 \ s}[/tex]
Solve the numerator.
3 m/s - 8 m/s = -5 m/s[tex]a=\frac{-5 \ m/s}{60 \ s}[/tex]
Divide.
[tex]a=-0.0833333333 \ m/s/s[/tex]
Let's round to the nearest hundredth.
The 3 in the thousandth place tells us to leave the 8 in the hundredth place.
[tex]a\approx -0.08 \ m/s^2[/tex]
The cyclist's acceleration is about [tex]\boxed {-0.08 m/s^2}[/tex]