Answer:
(a) 1, average velocity = -65.6 m/s
2, average velocity = -64.8 m/s
3, average velocity = -64.16 m/s
(b) The instantaneous velocity is -96 m/s
Explanation:
(a)
Average velocity is given by;
[tex]y(t_2,t_1) = \frac{y(t_2) - y(t_1)}{t_2-t_1}[/tex]
(1)
[tex]y(2.1,2) = \frac{(235-16*2.1^2) - (235-16*2^2)}{2.1-2}\\\\ y(2.1,2) = -65.6 \ m/s[/tex]
(2)
[tex]y(2.05,2) = \frac{(235-16*2.05^2) - (235-16*2^2)}{2.05-2}\\\\ y(2.05,2) = -64.8 \ m/s[/tex]
(3)
[tex]y(2.01,2) = \frac{(235-16*2.01^2) - (235-16*2^2)}{2.01-2}\\\\ y(2.01,2) = -64.16 \ m/s[/tex]
b. y = 235 - 16t²
The instantaneous velocity is given by;
v = dy /dt
dy / dt = -32t
when t = 3 s
v = -32(3)
v = -96 m/s
(a)The average velocity for the 0.1 sec,0.05 sec,0.01 sec will be -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.
What is the average velocity?The total displacement traveled by an object divided by the total time taken is the average velocity.
Average velocity is given by;
[tex]\rm y(t_2,t_1)=\frac{y(t_2)-y(t_1)}{t_2-t_1} \\\\[/tex]
The average velocity for case 1;
[tex]\rm y(2.1,2)=\frac{(235-16\times 2\times 1^2)-(235-16 \times 2^2)}{2.1-2} \\\\ \rm y(2.1,2)=\-65.6 \ m/sec[/tex]
The average velocity for case 2;
[tex]\rm y(2.015,2)=\frac{(235-16\times 2.05^2)-(235-16 \times 2^2)}{2.05-2} \\\\ \rm y(2.1,2)=\-64.8 \ m/sec[/tex]
The average velocity for case 3;
[tex]\rm y(2.01,2)=\frac{(235-16\times 2.01^2)-(235-16 \times 2^2)}{2.01-2} \\\\ \rm y(2.1,2)=\-64.16 \ m/sec[/tex]
Hence the average velocity for the 0.1 sec,0.05 sec,0.01 sec will be -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.
(b) The instantaneous velocity will be -96 m/s.
The given equation in the problem is;
[tex]\rm y = 235 - 16t^2[/tex]
The instantaneous velocity is given as;
[tex]v = \frac{dy}{dt} \\\\ \frac{dy}{dt} = -32t\\\\ t = 3 s\\\\ v = -32\times 3\\\\ v = -96 m/s[/tex]
Hence the instantaneous velocity will be -96 m/s.
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Which is the most dense solid?
Answer:
Bolt
Explanation:
Trevor and Nick are taxi drivers. Trevor drives a taxi using diesel oil while Nick drives a taxi using LPG. Whose taxi will cause higher levels of air pollution and why?
Answer:
Trevor's taxi would cause higher levels of air pollution
Explanation:
Trevor's taxi use diesel oil.
Diesel is less cleaner than LPG.
Compared to automotive pollution from petrol and diesel, pollutants from LPG-driven cars include lower amounts of petroleum hydrocarbons, nitrogen oxides , sulphur oxides, ozone contamination and particulate matter.
Tony completed a 720 km journey with an average speed of 90 km/h for the first 285 km he travelled at an average speed of 95 Km/h what was the average speed for the remaining journey
Answer:
[tex]Speed = 87 km/h[/tex]
Explanation:
Given
Total Distance = 720km
Average Speed = 90km/h
Average Speed (285km) = 95km/h
Required
Determine the average speed for the rest of the journey
First we need to determine the time taken to complete the journey using
[tex]Speed = \frac{Distance}{Time}[/tex]
[tex]90 = \frac{720}{Time_1}[/tex]
Make Time the subject of formula
[tex]Time_1 = \frac{720}{90}[/tex]
[tex]Time_1 = 8 hour[/tex]
Next, we determine the time taken to complete 285km of the journey using
[tex]Speed = \frac{Distance}{Time}[/tex]
[tex]95 = \frac{285}{Time_2}[/tex]
Make Time the subject of formula
[tex]Time_2 = \frac{285}{95}[/tex]
[tex]Time_2 = 3 hours[/tex]
The difference between these calculated times is the time taken to complete the rest of the journey
[tex]Time = Time_1 - Time_2[/tex]
[tex]Time = 8\ hour - 3\ hour[/tex]
[tex]Time = 5\ hour[/tex]
Also, we need to calculate the distance of the rest of the journey
[tex]Distance = 720\ km - 285\ km[/tex]
[tex]Distance = 435\ km[/tex]
The average speed can then be calculated;
[tex]Speed = \frac{Distance}{Time}[/tex]
[tex]Speed = \frac{435}{5}[/tex]
[tex]Speed = 87 km/h[/tex]
Hence, the average speed of the rest of the journey is 87km/h
What is the equation of the line on the graph?
A container weighs 450 lb when filled with 4 ft3 of fluid. If the empty container weighs 50 lb, determine the specific weight, mass density and specific gravity of this fluid.
Answer:
112.5 lb/ft³
405.93 kg/m³
0.406
Explanation:
given that
Weight of the container, w(c) = 450 lb
Volume of fluid, v(f) = 4 ft³
Weight of empty container, w(e) = 50 lb
Specific weight is said to be the weight per unit volume. Thus, the specific weight of this fluid is
w(s) = 450 / 4
w(s) = 112.5 lb/ft³
Mass density is the ratio of the mass of the fluid, with respect to the volume.
ρ = m/v
Since the question gives us the mass in weight, we'd have to convert it to mass from weight.
mass = weight / acceleration due to gravity
mass = 450 / 9.81
mass = 45.87 kg
Also, since the mass is going to be in kg, the volume also has to be in m³, thus needing a conversion.
4 ft³ = 0.113 m³
Mass density = 45.87 / 0.113
Mass density = 405.93 kg/m³
Specific gravity of the fluid is simply given as mass density / 1000. Therefore,
g(s) = 405.93 / 1000
g(s) = 0.406
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Two vectors of magnitudes |A| = 8 units and |B| = 5 units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A + B CANNOT have the value of:
The question is missing the alternatives. Here is the complete question.
Two vectors of magnitude |A| = 8units and |B| = 5units make an angle that can vary from 0° to 180°. The magnitude of the resultant vector A+B CANNOT have the value of:
A. 2 units
B. 5 units
C. 8 units
D. 12 units
Answer: A. 2 units
Explanation: Vector is an entity that has characteristics as magnitude and direction. Resultant vector is the "sum" of 2 or more vectors.
In this question, the vectors have magnitude and angle varies from 0° to 180°.
When angle between vectors A and B is 0°, they are parallel and pointing to the same direction, so:
[tex]V_{R} = |A| + |B|[/tex]
[tex]V_{R}=8+5[/tex]
[tex]V_{R}[/tex] = 13
When the angle is 180°, it means vectors are in opposing directions, so:
[tex]V_{R} = |A| - |B|[/tex]
[tex]V_{R} = 8-5[/tex]
[tex]V_{R}[/tex] = 3
From the calculations, we can conclude the magnitude of resultant vector varies between 3 and 13.
The least value is 3, so it cannot have a value of 2 units.
a) An electric circuit is rates, 240V, 13Ω calculate the amount of current that can be used by this appliance.
Answer:
18.4615385 amps
Explanation:
The voltage V in volts (V) is equal to the current I in amps (A) times the resistance R in ohms (Ω):
If you want to replicate another scientist's experiment, which sections of their laboratory report will provide you with the most valuable information?
A person with a black belt in taekwondo has a foot with a mass of 0.90 kg. Starting from rest, this foot attains a velocity of 8.3 m/s in 0.13 s. What is the magnitude of the average net force applied to the foot to obtain that acceleration?
Answer:
57.42 N
Explanation:
We first find the acceleration knowing that it goes from rest to 8.3 m/s in 0.13 seconds,
Therefore, the acceleration is:
[tex]a=\frac{v_f-v_i}{time} =\frac{8.3-0}{0.13 } =63.8\,\,m/s^2[/tex]
Now we use this to calculate the average net force by multiplying mass times acceleration:
F = m * a = 0.9 (63.8) = 57.42 N
What is the magnitude of total charge of all the electrons in 1.2 L of liquid water?
Answer:
6.416*10^ 8C
Explanation:
First we find mass of the water
Mass= density x volume
=1.2*1000= 1200g
To find number of moles we use
N= mass/ molar mass
= 1200/18.02= 66.6mol
So the total number of water molecules is
66.6* 6.022*10^23= 401.07x 10^23moles
But each h20 moles has 10 electrons so it will be 4.01*10^26electrons
Then finally total charge will be
4.01*10^26electrons x 1.6*10^-19
= 6.416*10^ 8C
The magnitude of total charge will be "6.416×10⁸ C".
Electrons:According to the question,
Density, d = 1.2 L
Volume, V = 1000
The mass will be:
→ Mass = Density × Volume
By substituting the values,
= [tex]1.2\times 1000[/tex]
= [tex]1200[/tex] g
Now,
The number of moles will be:
→ N = [tex]\frac{Mass}{Molar \ mass}[/tex]
= [tex]\frac{1200}{18.02}[/tex]
= [tex]66.6[/tex] mol
The total no. of water molecules be:
= [tex]66.6\times 6.022\times 10^{23}[/tex]
= [tex]401.07\times 10^{23}[/tex] moles
hence,
The total charge be:
= [tex]4.01\times 10^{26}\times 1.6\times 10^{-19}[/tex]
= [tex]6.416\times 10^8[/tex] C
Thus the above response is correct.
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Maddie Cat can ride her tricycle at an amazing speed of 3.75 meters per second.
How far can she go in 5.0 seconds?
Distance = (speed) x (time)
Distance = (3.75 m/s) x (5.0 s)
Distance = 18.75 meters
Answer: 3.75 x 5.0= 18.75 meters
Explanation:
If a gannet hits the water at 32 m/s, what height did it dive from? Assume that the gannet was motionless before starting its dive.
Answer:
The value is [tex]h = 52.2 \ m[/tex]
Explanation:
From the question we are told that
The velocity at which he hit the water is [tex]v = 32 \ m/s[/tex]
Generally from kinematic equation
[tex]v^2 = u^2 + 2gh[/tex]
Here the initial velocity u = 0 m/ given that the gannet started the jump from rest.
=> [tex]32^2 = 0^2 + 2*(9.8)h[/tex]
=> [tex]h = 52.2 \ m[/tex]
Can an objects displacement be greater than or equal to the objects distance?
If an X-ray tube is operating at a current of 30.0 mA:a) How many electrons are striking the target per second? b) If the potential difference between the anode and cathode of this tube is 100.0 kV, how much power is expended
Answer:
Explanation:
A. Q= It
30E-3A=q
Ne = q
30E-3/1.6*10-19= N
N= 1.8*10^16 electrons
B. Power= I x v
= 30*10^-3A x 100*10^3v
= 3000watts
Would a human feel more gravity on a bigger planet or less gravity
Answer: you would feel more gravity
Explanation: the more mass of an object the more pull
How does the Coriolis effect impact ocean currents in the Northern and Southern Hemispheres?
Now let’s pretend you’re standing at the North Pole. When you throw the ball to your friend, it will again to appear to land to the right of him. But this time, it’s because he’s moving faster than you are and has moved ahead of the ball.
Everywhere you play global-scale "catch" in the Northern Hemisphere, the ball will deflect to the right.
assume this car is driven off a cliff. How many arrows of force need to be drawn in the free body diagram? Assum no air resistance
Answers:
five
one
four
three
Answer:
4
Explanation:
friction
weight
normal reaction
force to overcome inertia
Answer:
1
Explanation:
--->
To practice Problem-Solving Strategy 22.1 for electric force problems. Two charged particles, with charges q1=qq1=q and q2=4qq2=4q, are located on the x axis separated by a distance of 2.00cm2.00cm . A third charged particle, with charge q3=qq3=q, is placed on the x axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3.Find the position of charge 3 when qqq = 2.00 nCnC .
Answer:
x₂ = 0.01336
Explanation:
In this exercise we use the translational equilibrium equation
F₁₃ - F₂₃ = 0
F₁₃ = F₂₃
at the point where charge 3 is placed the two electric forces have the same magnitude
let us use the expression of Coulomb's law for the electric force
F₁₃ = ka q₁ q₃ / r₁₃²
F₂₃ = ka q₂ q₃ / r₂₃²
we substitute
k q₁ q₃ / r₁₃² = k q₂ q₃ / r₂₃²
now imprescriptibility suppose that particle 1 is at the origin of the coordinate system, particle 2 is at a distance d = 2.00cm = 2 10-2 m, therefore let's call the distance from particle 1 to particle 3 as x
r₁₃ = x
R₂₃ = d-x
In the exercise we are given the charges for the particle1 q1 = q, for the particle 2 the charge is q2 = 4q the distance between them is d = 2.00cm = 0.0200 m, the value of q = 2.00 nC = 2.00 10⁻⁹ C
let's substitute these values
q₁ / x₂ = q₂ / (d-x)²
let's clear x
(d-x)² = q₂ / q₁ x²
d² - 2dx + x₂ = q₂ /q₁ x²
x² (1-q₂ / q₁) - 2d x + d² = 0
let's substitute the values and solve the quadratic equation
x² (1 - 4q / q) - 2 0.02 x + 0.02² = 0
-3 x² - 0.04 x + 0.0004 = 0
x² + 0.0133 x - 0.0001333 = 0
x = [-0.0133 ±√(0.0133² + 4 0.00013333)] / 2
x = [-0.0133 + - 0.026664] /2
x₁ = -0.01998 m
x₂ = 0.01336 m
Since load 3 must be between charged 1 and 2 the correct answer is
x₂ = 0.01336
Explain why a golf ball has a higher density than a ping pong ball, even though they are similar in size and shape.
Answer:
The ping pong ball is hollow.
Explanation:
Since a ping pong ball, unlike the golf ball, is only filled with air, it is less dense. Air is notably LESS dense than solids, which is what comprises the inside of a golf ball.
What net force is needed to accelerate a 1.25 kg book 5.00 m/s2?
Answer:
F = 6.25 N
Explanation:
Given that,
Mass of the book is 1.25 kg
Acceleration of the book is 5 m/s²
We need to find the net force needed to accelerate the book. Net force is given by :
F = ma
[tex]F=1.25\times 5\\\\F=6.25\ N[/tex]
So, 6.25 N of force is acting on the book.
The fastest land animal is the cheetah. A cheetah can run 100 meter dash in 5.95 seconds, calculate the cheetahs average speed in meters per second
Answer:
16.80672269 m/s
Explanation:
100 divide by 5.95 seconds
Answer:
16.8m/s
Explanation:
S=D/T
=
[tex] \frac{100}{5.95} [/tex]
=16.80672269
=16.8
Which is true for a car moving around a circular track with constant speed? 1. It has zero acceleration2. it has an acceleration directed toward the center of its path3. it has an acceleration directed away fromt he center of its path4. it has an acceleration with a direction that cannot be determined from the information given5. it has an acceleration component in the direction of its velocity.
Answer:
2. it has an acceleration directed toward the center of its path
Explanation:
For a car moving with constant velocity around a circular track, there is a a change in the direction of the velocity at every point on the path taken by the car around the track. This change in direction generates an acceleration on the car which will be directed towards the center of the track. This is why the inertia force on a person inside the car when it is driven around a circular track is usually away from the center of the track, since the inertia force acts in an opposite direction to the acceleration on a body.
How does diet affect diabetes
Answer:
A diet high in fat, calories, and cholesterol increases your risk of diabetes. A poor diet can lead to obesity (another risk factor for diabetes) and other health problems. A healthy diet is high in fiber and low in fat, cholesterol, salt, and sugar. Also, remember to watch your portion size.
A flag pole is attached to the side of a building 5.00 ft off the ground and it hangs down 30 degrees from the vertical. If the pole is 6.00 ft in length, how high in feet is the top of the pole at its highest point (sticking out from building)? (Hint: draw a picture) E
Answer:
h ’= 0.6963 m
this is the height of the part of the post it supports.
Explanation:
For this exercise we can use the trigonometric relationships
Let's start by finding the vertical component of the height of the pole
cos 30 = x / L
x = L cos 30
x = 6 cps 30
x = 5.196 m
with this length, the post has the same height as the building, so there are
Aₓ = L -x
Δx = 6 -5.196
Δx = 0.804 ft
the height of this section is
cos 30 = h ’/ Dx
h ’= 0.804 cos30
h ’= 0.6963 m
this is the height of the part of the post it supports.
Please help!
A tennis ball falls off a shelf and bounces several times. Each bounce is lower than the one before. Soon the ball stops. Why doesn’t the ball keep bouncing?
A) some of the energy is changed into mass
B) The energy becomes stored in the ball
C) Energy is transferred to the air and ground
Answer:
c
Explanation:
energy isn't stored and it doesn't change to mass
The ball has some kinetic energy when it hits the floor, but some of it is changed, so it loses some of it each time it bounces. After a few bounces, the ball has so little kinetic energy remaining that it stops bouncing. Thus, option C is correct.
What doesn’t the ball keep bouncing?Since the gravitational potential energy, which can be transformed back into kinetic energy on the rebound, increases with the drop height, the consequent bounce height will likewise rise.
Because it has the most elasticity, the rubber ball will rebound the highest when all three balls are dropped from the same height. Because rubber is incredibly elastic, it squishes or compresses as it touches the ground but immediately snaps back to its original shape.
Therefore, Additionally, some energy is changed into other forms like heat and sound. The majority of these additional energy sources are lost and not recovered, causing the ball to bounce back to a lesser height.
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If you do not have enough time to complete a full workout, you should:
A. Cut the cool-down portion short.
B. Skip the warm-up and cool-down portions altogether.
C. Cut the warm-up portion short.
D. Cut the exercise portion short.
Answer:
the answer to this question would be cut the exercise portion down (D)
this is because warm ups and cooling down during exercise are more important than the exercise itself
Explanation:
Starting from rest, a panther accelerates at 3 m/s/s for 10 seconds. What is the final velocity of the panther
Answer:
Final velocity = 30 m/s
Explanation:
We are given;
Initial velocity; u = 0 m/s
Acceleration; a = 3 m/s²
Time; t = 10 seconds
From Newton's first law of motion, the final velocity is given by the formula;
v = u + at
Plugging in the relevant values gives;
v = 0 + (3 × 10)
v = 30 m/s
How does society shape reality?
A particle makes 240 revolutions per minute on a circle of radius 2m. Find I. its period ii. angular velocity III. linear velocity.
Answer:
(i) The period, T is 0.25 s
(ii) The angular velocity, ω is 25.136 rad/s
(iii) The linear velocity is, v is 50.27 m/s
Explanation:
Given;
number of revolution of the particle, N = 240 revolutions per minutes
radius of the circle, R = 2m
(i) The period is given by;
[tex]T = \frac{2\pi}{\omega}[/tex]
where;
ω is angular velocity
[tex]\omega = (240 \frac{rev}{min}) *(\frac{1 \ min}{60 \ s} )*(2\pi \frac{rad}{rev})\\\\ \omega = 25.136 \ rad/s[/tex]
[tex]T = \frac{2\pi }{\omega}\\\\ T = \frac{2\pi}{25.136}\\\\T = 0.25 \ s[/tex]
(ii) angular velocity, ω = 25.136 rad/s
(iii) linear velocity is given by;
v = ωR
v = (25.136 rad/s) x (2 m)
v = 50.27 m/s
What two processes are involved in the formation of Earth’s magnetic field?
Answer:
i. Geodynamo
ii. Gravitational energy conversion
Explanation:
The outer core of the Earth is believed to be in molten form, consisting of mainly iron and nickel. The reaction (mixture) between these components or elements generates conventional currents which is maintained by the gravitational energy produced in the process. Thus, magnetic fields are generated continuously due to the continuous flow of electric current during the processes.