Answer: 5.5m/s
Explanation:
vf=vi+at
vf= 4.0m/s + (0.50m/s^2)(3.0s)
The speed of the cart at the end of this 3.0 second interval is 5.5 meter per seconds.
Given the following data:
Initial velocity = 4 m/sMass of cart = 6 KgAcceleration = 0.5 [tex]m/s^2[/tex]Time = 3 secondsTo find the speed of the cart at the end of this 3.0 second interval, we would use the first equation of motion;
[tex]V = U + at[/tex]
Where:
U is the initial velocity.V is the final velocity. a is the acceleration. t is the time measured in seconds.Substituting the given parameters into the formula, we have;
[tex]V = 4 + 0.5(3)\\\\V = 4 + 1.5[/tex]
Final velocity, V = 5.5 m/s.
Therefore, the speed of the cart at the end of this 3.0 second interval is 5.5 meter per seconds.
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Which of the following descriptions best describe a liquid
A
takes the shape and volume of its container
B
matter is made of atoms so tightly packed together that they cannot move around
C
has a definite volume, but takes the shape of its container
Answer:
C
Explanation:
Show the relation among MA, VR and n.
Answer:
good luck!!! sorry I just needed the points xoxo
Explanation:
umm yeah no sorry I tried
You want to lean your dad's ladder on a smooth wall. If the mass of ladder is 4.42 kg and coefficient
of friction of the floor is 0.53, what is the minimum angle, theta-min at which the ladder does nofip? What
do you think the maximum angle theta-max could be? Sketch and label your free body diagram.
(5 marks)
Answer:
angle minimum θ = 41.3º
Explanation:
For this exercise let's use Newton's second law in the condition of static equilibrium
N - W = 0
N = W
The rotational equilibrium condition, where we place the axis of rotation on the wall
We assume that counterclockwise rotations are positive
fr (l sin θ) - N (l cos θ) + W (l/2 cos θ) = 0
the friction force formula is
fr = μ N
fr = μ W
we substitute
μ m g l sin θ - m g l cos θ + mg l /2 cos θ = 0
μ sin θ - cos θ + ½ cos θ= 0
μ sin θ - ½ cos θ = 0
sin θ / cos θ = 1/2 μ
tan θ = 1/2 μ
θ = tan⁻¹ (1 / 2μ)
θ = tan⁻¹ (1 (2 0.57))
θ = 41.3º
that delivers oxygen to your body and In the video your blood is compared to a picks up CO2 to be released out when you breath. PLEASE I NEED A ANSWER
At an accident scene on a level road, investigators measure a car's skid mark to be 98 m long. It was a rainy day and the coefficient of friction was estimated to be 0.38. a) Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.b) Why does the car's mass not matter?
Answer:
a. V = 19.1m/s
b. The mass of the car does not matter
Explanation:
A.
KE = 1/2mv² = fd --------(1)
Fd = umgd ---------(2)
Therefore,
1/2mv² = umgd ---------(3)
M will cancel itself out from both sides of equation 3.
Then we will have:
1/2v² = ugd
Then we cross multiply to make v² the subject of the formula
V² = 2ugd
V = √2ugd -------(4)
U = 0.38
g = 9.81
d = 98
When we input these values into equation 4, we will have:
V = √2x0.38x9.81x98
V = √730.6488
V = 27.03m/s
B.
The mass of the car does not actually matter as the mass was cancelled out on the both sides of equation 3
A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.
Answer:
m = 876.71 kg
Explanation:
This is an exercise of Archimedes' principle, which states that the thrust on a body is equal to the weight of the dislodged liquid
B = ρ g V
therefore the load that the balloon can lift is
B - W_structure - w_load = 0
w_load = B - W_structure
The volume of the balloon is
v = 4/3 π r³
let's substitute
w_carga = rho g 4/3 π r³ - m_structure g
the air density at T = 25ºc is ρ = 1.18 kg / m³
let's calculate
w_load = 1.18 9.8 4/3 π 7.15³ - 930 9.8
w_load = 17705,77 - 9114
w_ load = 8591.77 N
this corresponds to a mass of
w_load = m g
m = w_load / g
m = 8591.77 / 9.8
m = 876.71 kg
Four balls have the same temperature. Which ball has the most thermal
energy?
A. Golf ball
B. Bowling ball
C. Tennis ball
D. Basketball
Answer:
a bowling ball because it has the most mass.
For satellite travelling on circular orbit if radius of the orbit increased 4 times then the period of the satellite increased *
2
4
8
none of the above
Answer:
8
Explanation:
An object that moves in uniform circular motion has a centripetal acceleration of 13 m/s^2 . If the radius of the motion is 0.02m, what is the frequency of motion?
Answer:
f = 3.97 Hz
Explanation:
Given that,
Centripetal acceleration, [tex]a=13\ m/s^2[/tex]
The radius of motion is 0.02 m
The formula for the centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}\\\\v=\sqrt{ar} \\\\v=\sqrt{13\times 0.02} \\\\v=0.5\ m/s[/tex]
The speed of an object in a circular path is given by :
[tex]v=\dfrac{2\pi r}{t}[/tex]
t is time period
Also, f=1/t (f is frequency)
[tex]f=\dfrac{v}{2\pi r}\\\\f=\dfrac{0.5}{2\pi \times 0.02}\\\\f=3.97\ Hz[/tex]
Hence, the frequency of motion s 3.97 Hz.
The frequency of the motion is 4.1 Hz.
Linear velocity?The linear velocity of the of the object is calculated as follows;
[tex]a = \frac{v^2}{r} \\\\v^2 = ar\\\\v = \sqrt{ar} \\\\v = \sqrt{13 \times 0.02} \\\\v = 0.51 \ m/s[/tex]
Angular speed of the objectThe angular speed of the object is calculated as follows;
[tex]\omega =\frac{v}{r} \\\\\omega = \frac{0.51}{0.02} \\\\\omega = 25.5 \ rad/s[/tex]
Frequency of motionThe frequency of the motion is calculated as follows;
[tex]\omega = 2\pi f\\\\f = \frac{\omega }{2\pi} \\\\f = \frac{25.5}{2\pi } \\\\f = 4.1 \ Hz[/tex]
Thus, the frequency of the motion is 4.1 Hz.
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Explane Hawaii characteristics
Answer:
Hawaii is located in the Pacific Ocean to the southwest of the continental U.S., southeast of Japan and northeast of Australia. Hawaii is known for its tropical climate, unique topography, and natural environment, as well as its multicultural population.
How many turns are needed in a solenoid of radius 10 cm and length 20 cm for its self-inductance to be 6.0 H?
A) 30
B) 74
C) 500
D) 550
E) 5500
Answer:
B
Explanation:
74 turns are needed in a solenoid of radius 10 cm and length 20 cm for its self-inductance to be 6.0 H
what is solenoid?The solenoid is a type of electromagnet and the main purpose of the solenoid is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
The solenoid is a coil structure of wire, and the plunger is made of soft iron. The magnetic field is formed around it when an electric current passes through it and draws the plunger in.
the solenoid is responsible for converting electrical energy into mechanical work, these were the results of the development of an efficient and greater strength offering magnets which was discovered in the year 1823.
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An unladen swallow that weighs 0.03 kg flies straight northeast a distance of 125 km in 4.0 hours. With the x x direction due east and the y y direction due north, what is the average momentum of the bird (in unit vector notation)?
Answer:
The average momentum of the bird is 0.26 kgm/s
Explanation:
The formula to be used here is that of momentum which is
momentum (in kgm/s) = mass (in kg) × velocity (in m/s)
The velocity of the bird is
velocity (in m/s) = distance (in meter) ÷ time (in seconds)
distance in meters = 125km × 1000 = 125,000 m
time in seconds = 4 hrs × 60 × 60 = 14,400 secs
velocity = 125000/14400
velocity = 8.68 m/s
momentum (p) = 0.03 × 8.68
p = 0.26 kgm/s
The average momentum of the bird is 0.26 kgm/s
The average momentum of the bird (in unit vector notation) is (0.1842i + 0.1842j) kgm/s.
Total displacementSince the unladen swallow that weighs 0.03 kg flies straight northeast (that is at a bearing of 45°) a distance of 125 km in 4.0 hours.
Its position vector after 4.0 hours is d = (125kmcos45)i + (125kmsin45)j = (125000 × 1/√2)i + (125000 × 1/√2)j
= (62500√2)i + (62500√2)j.
If the initial position of the swallow is d' = 0i + 0j, then its total displacement after 4 hours is, D = d - d'
= (62500√2)i + (625000√2)j - (0i + 0j)
= (62500√2)i + (62500√2)j m
Average velocityThe unladen swallow's average velocity, v = D/t where
D = total displacement = (62500√2)i + (62500√2)j m and t = time = 4.0 hours = 4 × 60 min/hr × 60 s/min = 14400 sSo, v = [(62500√2)i + (62500√2)j m]/14400 s = (88388.35)i/14400 + (88388.35)j /1440
= 6.14i + 6.14j m/s
Average momentumThe average momentum of the unladen swallow is p = mv where
m = mass of unladen swallow = 0.03 kg and v = average velocity = 6.14i + 6.14j m/sSo, p = mv
p = 0.03 kg × (6.14i + 6.14j m/s)
p = (0.1842i + 0.1842j) kgm/s
So, the average momentum of the bird (in unit vector notation) is (0.1842i + 0.1842j) kgm/s.
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3.
A net force acting on an 8.0 kg box produces an acceleration of 3.5 m/s2. What acceleration will the same net force cause to a different box with a mass of 2.0 kg?
Answer:
13.5
Explanation:
The acceleration that the same net force would cause to a different box is 14 [tex]m/s^2[/tex].
Given the following data:
Mass of box A = 8 kg
Acceleration = 3.5 [tex]m/s^2[/tex]
Mass of box B = 2 kg
To find the acceleration that the same net force would cause to a different box:
First of all, we would determine the net force acting on box A by applying Newton's Second Law of Motion.
Mathematically, Newton's Second Law of Motion is given by the formula;
[tex]Net\;force = mass \times acceleration\\\\Net\;force = 8 \times 3.5[/tex]
Net force = 28 Newton.
Now, we can determine the acceleration for box B since the same net force act on it.
[tex]Acceleration = \frac{Net\;force}{mass} \\\\Acceleration = \frac{28}{2 }[/tex]
Acceleration = 14 [tex]m/s^2[/tex]
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laser beam is incident on two slits with a separation of 0.195 mm, and a screen is placed 5.10 m from the slits. If the bright interference fringes on the screen are separated by 1.61 cm, what is the wavelength of the laser light?
Answer:
615 nm
Explanation:
The separation between the two slits, d = 0.195 mm = [tex]0.195\times 10^{-3}\ m[/tex]
The bright interference fringes on the screen are separated by 1.61 cm, [tex]\Delta y=1.61\ cm=0.0161\ m[/tex]
Distance between the screen and the slit, D = 5.1 m
We need to find the wavelength of the laser light. The separation between two bright interference fringes is given by:
[tex]\Delta y=\dfrac{\lambda D}{d}\\\\\lambda=\dfrac{\Delta y d}{D}\\\\=\dfrac{0.0161\times 0.195\times 10^{-3}}{5.1}\\\\=6.15\times 10^{-7}\ m\\\\=615\ nm[/tex]
So, the wavelength of the laser light is 615 nm.
Suppose that an object undergoes simple harmonic motion, and its displacement has an amplitude A = 15.0 cm and a frequency f = 11.0 cycles/s (Hz). What is the maximum speed ( v ) of the object?
A. 165 m/s
B. 1.65 m/s
C. 10.4 m/s
D. 1040 m/s
Answer:
Maximum speed ( v ) = 10.4 m/s (Approx)
Explanation:
Given:
Amplitude A = 15.0 cm = 0.15 m
Frequency f = 11.0 cycles/s (Hz)
Find:
Maximum speed ( v )
Computation:
Angular frequency = 2πf
Angular frequency = 2π(11)
Angular frequency = 69.14
Maximum speed ( v ) = WA
Maximum speed ( v ) = 69.14 x 0.15
Maximum speed ( v ) = 10.371
Maximum speed ( v ) = 10.4 m/s (Approx)
The purpose of a motor is to:
A. convert electrical energy to mechanical energy.
B. provide a safe circuit for current flow.
C. convert electrical energy to nuclear energy.
D. convert chemical energy to electrical energy.
Answer:
a motor is used to covert electrical energy to mechanical energy
7) A moving object is rolling on a surface that is 5 m off the ground. The object is moving at a constant speed of 4 m/s. If the object is 3.2 kg, what is the final energy of the ball after rolling for 10 m, assuming friction is negligible?
156.8 J
131.2 J
182.4 J
25.6 J
8) A spreadsheet application is used to create a computational model of the energy experienced by a pendulum. How do the energy values of the pendulum relate?
The sum of the potential energy and the kinetic energy is always constant.
The sum of the potential energy and the kinetic energy is always 0.
The potential energy is always greater than the kinetic energy.
The kinetic energy is always equal to the potential energy.
131.2 J and The last one on number 8
I gave the same answer and it passed.
7) The final energy of the ball after rolling for 10 m is 182.4 J so, option C is correct.
8) When friction is negligible the total energy is the sum of kinetic and potential energy is constant so, option A is correct.
What is energy?Energy is the ability to perform work in physics. It could exist in several different forms, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc. Additionally, there is heat and work, which is energy being transferred from one body to another.
Given:
A moving object is rolling on a surface that is 5 m off the ground,
The speed of the object, v = 4 m/s,
The mass of the object, m = 3.2 kg,
Calculate the kinetic energy after 10 meters as shown below,
KE = 1/2 × 4² × 3.2
KE = 25.6 J
Calculate the potential energy as shown below,
PE = 3.2 × 9.8 × 5
PE = 156.8 J
Thus, total energy = KE + PE
The total energy = 25.6 + 156.8
The total energy = 182.4 J
8) when there is no resistance. Combined mechanical energy I.e. the total amount of kinetic and potential energy is constant.
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What is the Poynting vector S⃗ (x,t)S→(x,t), that is, the power per unit area associated with the electromagnetic wave described in the problem introduction
Answer:
[tex]\mathbf{S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i }[/tex]
Explanation:
Consider:
[tex]E^{\to} =E_o \ Sin (kx - wt) \hat j[/tex]
[tex]B^{\to} =B_o \ Sin (kx - wt) \hat k[/tex]
The equation for the Poynting vector is given as:
[tex]S^{\to} (x,t) = \dfrac{E^{\to}\times B^{\to}}{\mu_o}[/tex]
[tex]S^{\to} (x,t) = \dfrac{E_o \ Sin(kx - wt) \hat j \times B_o sin (kx -wt) \hat k}{\mu_o}[/tex]
[tex]S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) (\hat j \times \hat k)[/tex]
[tex]S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i[/tex]
∴
[tex]\mathbf{S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i }[/tex]
A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a light bulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2.00 m from the light bulb?
A) 15 W/m2
B) 4.8 W/m2
C) 2.4 W/m2
D) 0.60 W/m2
E) 1.2 W/m2
Answer:
a
Explanation:
A 60-W light bulb emits spherical electromagnetic waves uniformly in all directions. If 50% of the power input to such a light bulb is emitted as electromagnetic radiation, what is the radiation intensity at a distance of 2.00 m from the light bulb
so i did 60(50%)=30÷2=15
The radiation intensity is 15 W / m².
To find the radiation intensity, the values are given as,
Power = 60 W
Distance = 2 m
50% of the power input is emitted as electromagnetic radiation.
What is radiation intensity?The amount of energy emitted per unit solid angle by per unit area of the radiating surface can be said as radiation intensity.
As, when there is a power output, the input power will emit some energy as a kinetic energy and electromagnetic radiation. By the way, the power input emits 50 % as a radiation, so the power input given as,
P = 60 / 2 ( As it was 50 % )
= 30 Watt.
The radiation intensity is,
In = 30 / 2
= 15 W / m².
Thus, the radiation intensity is calculated as, 15 W/ m².
So, Option A is the correct answer.
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A car traveling initially at a speed of 20 m/s accelerates to a speed of 31 m/s over a distance of 45 meters.
What is the magnitude of the car's acceleration?
Answer:abc defg hijk lmnop qrs tuv wx y and z
Explanation: now i know my abc's
Help me please!
On the earth, the gravitational field strength is 10 N/kg. On the Moon, the gravitational field strength is 1.6 N/kg.
If an object has a weight of 50 N on earth, what is its weight on the Moon?
A: 1.6 N
B: 5.0 N
C: 8.0 N
D: 80 N
Answer:
This is a way of measuring how much gravity there is. The formula is: weight/mass = gravitational field strength.
Gravitational field strength = Weight/mass unit is N/kg
Weight = mass x gravitational field strength unit is N
On Earth the gravitational field strength is 10 N/kg. Other planets have different gravitational field strengths. The Moon has a gravitational field strength of 1.6 N/kg. You might have seen films of astronauts leaping high on the moon.
Here on Earth, if I jump I am pulled back to ground by gravity. What is my weight? My mass is 80kg and if we multiply by gravitational field strength (10N/kg) - my weight is 800N. Now if I go to the moon, my mass will be the same, 80kg. We multiply that by the moon's gravitational field strength, which is 1.6 N/ kg. That means my weight on the moon is 128N. So I have different weights on the Earth and on the Moon. That's why astronauts can jump high into the air on the moon - they're lighter up there.
Jupiter is a very large planet with strong gravitational field strength of 25 N/ kg. My body is 80kg. If I go to Jupiter my weight is going to be 25 x 80 = 2,000 N. That means I wouldn't be able to get off the ground or stand up straight! I would probably be lying down all the time there. So weight varies depending on which planet you are on. You can find out more yourself by looking up tables of weight on different planets.
A plane flying at a speed of 59.1 m/s is dropping a package 521 m above the intended target. How long does it take for the package to hit the ground?
A.) 10.3 seconds
B.) 0.1 seconds
C.) 106.3 seconds
D.) 8.8 seconds
Answer:
t = 10.31 seconds which agrees with answer option A)
Explanation:
Notice that the horizontal velocity of the plane imparted to the package, doesn't affect the vertical motion for which the original (vertical velocity) is zero.
Then the equation for the distance travelled by the package is:
d = (1/2) a t^2
in our case, d = 521 m, and a = g (acceleration of gravity 9.8 m/s^2)
then we can solve for t in the equation:
521 = 9.8/2 t^2
t^2 = 521/4.9
t^2 = 106.32 s^2
t = 10.31 seconds
Which of the following are electromagnetic waves?a. Water wavesb. Radio wavesc. Sound wavesd. Seismic waves
Answer:
Radio waves
Explanation:
Radio wavs are electromagnetic waves.
Hope this helped!
How are the toes of a hen different from that of an eagle?
Answer:
no they different
Explanation:
because hen lives on land and eagle flies in sky it doesnt walk often just it aearch for its prey and it eats there only
Answer:
eheisjsnsndndj
Explanation:
sjdjdj
Write the function y(x, t) that describes this pulse if it is traveling in the positive x-direction with a speed of 2.10 m/s. (Use the following as necessary: x and t. Assume x and y are in meters and t is in seconds. Do not include units in your answer.) y(x, t) = _______.
Answer:
The function is missing in the question. The function of the transverse pulse in the wire is given by [tex]$y=\frac{6}{x^2 +3}$[/tex]
Explanation:
A transverse wave can be defined as the wave whose direction of displacement is always perpendicular to the direction of propagation. For example, surface wave at water bodies. While a pulse can be defined as a sudden change in a constant quantity such as a pulse of the radiation or current.
Let the wire of infinite length in both the directions and also the magnitude of deflection of wire be in the same shape except the point of maximum deflection to move along the wire.
Thus the equation of the pulse moving the in the positive x-direction moving at the speed of 2.10 m/s is
[tex]$y=\frac{6}{(x-2.10)^2 +3}$[/tex].
What is the magnitude and direction of the magnetic force on the bob at the lowest point in its path, if it has a positive 0.250 μC charge and is released from a height of 30.0 cm above its lowest point? The magnetic field strength is 1.50 T.
Answer:
[tex]F=9.09\times 10^{-7}\ N[/tex]
Explanation:
Given that,
Charge, q = 0.250 μC
It is released from a height of 30 cm or 0.03 m
The magnetic field strength is 1.50 T.
First we find the velocity using the conservation of energy as follows :
[tex]mgh=\dfrac{1}{2}mv^2\\\\v=\sqrt{2gh} \\\\v=\sqrt{2\times 9.8\times 0.3} \\\\v=2.424\ m/s[/tex]
Now, the magnetic force is given by :
[tex]F=qvB\\\\=0.25\times 10^{-6}\times 2.424\times 1.5\\\\=9.09\times 10^{-7}\ N[/tex]
So, the magnetic force is [tex]9.09\times 10^{-7}\ N[/tex]. Since, the bob is at the lowest point, the direction of the magnetic force at the lowest point is upward.
An object has a mass of 15 kg and is accelerating to the right at 16.3 m/s2. The free-body diagram shows the horizontal forces acting on the object. A free body diagram with 2 forces. The first vector is pointing right, labeled F Subscript a Baseline 250 N. The second vector is shorter pointing left, labeled F Subscript f Baseline. What is the frictional force, Ff, acting on the object?
Answer:
A. -5.5 N
Explanation:
I can confirm that the answer is A.
The components of vector Upper A Overscript right-arrow EndScripts are Ax and Ay (both positive), and the angle that it makes with respect to the positive xaxis is θ. Find the angle θ if the components of the displacement vector Upper A Overscript right-arrow EndScripts are:
(a) Ax = 12 m and Ay = 12 m,
(b) Ax= 19 m and Ay = 12 m, and
(c) Ax = 12 m and Ay = 19 m.
(a) θ = Number____________ Units____
(b) θ = Number____________ Units____
(c) θ = Number ____________Units____
Answer:
(a) θ = 45° = 0.78 rad
(b) θ = 32.27° = 0.56 rad
(c) θ = 57.27° = 1 rad
Explanation:
When a vector is resolved into its rectangular components, the formula for the direction angle of the vector with positive x-axis is given as:
tan θ = Ay/Ax
θ = tan⁻¹(Ay/Ax)
(a)
Ax = 12 m
Ay = 12 m
θ = tan⁻¹(12 m/ 12 m)
θ = tan⁻¹(1)
θ = 45° = 0.78 rad
(b)
Ax = 19 m
Ay = 12 m
θ = tan⁻¹(12 m/19 m)
θ = tan⁻¹(0.6315)
θ = 32.27° = 0.56 rad
(c)
Ax = 12 m
Ay = 19 m
θ = tan⁻¹(19 m/12 m)
θ = tan⁻¹(1.58333)
θ = 57.27° = 1 rad
Question 1 of 5
In which way are electromagnetic waves different from mechanical waves?
Answer:
Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.
Explanation:
Answer:
In which way are electromagnetic waves different from mechanical waves?Electromagnetic waves can travel through empty space
Explanation:
I took A P E X Quiz.
A cyclist is riding along at a speed of 20.7 when she decides to apply the brakes which gave a deceleration applied was a rate of -3.4 m/s2 over the span of 7.8 s. What distance does she travel over that period of time.
Answer:
The distance is 58.03 m
Explanation:
Constant Acceleration Motion
It occurs when the velocity of an object changes by an equal amount in every equal period of time.
Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:
[tex]v_f=v_o+at[/tex]
The distance traveled by the object is given by:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}[/tex]
The conditions of the problem state the cyclist has an initial speed of v0=20.7 m/s during t=7.8 seconds and acceleration of -3.4 m/s^2.
The final speed is:
[tex]v_f=20.7+(-3.4)\cdot 7.8[/tex]
[tex]v_f=20.7-26.52[/tex]
[tex]v_f=-5.82\ m/s[/tex]
Note the cyclist has stopped and come back because his speed is negative. Now calculate the distance:
[tex]\displaystyle x=20.7\cdot 7.8+\frac{(-3.4)\cdot 7.8^2}{2}[/tex]
[tex]\displaystyle x=161.46-103.43[/tex]
x=58.03 m