A truck is traveling at a constant speed of 20 m/s through a school zone. At time t = 0 seconds, he passes a hidden police car that is at rest. Five seconds after the truck passes, the police car begins accelerating at a constant rate of 2 m/s in order to catch the truck.

Determine the time at which the speed of the truck is equal to the speed of the police car. Mark this time as t↓1. How will the positions of the police car and the truck compare when they have the same speed and why?​

Answers

Answer 1

Answer:

Let's define:

The position zero will be in the first point where the truck and police car meet. (So the initial position of both vehicles is zero)

Then, the position equation for the truck is:

T(t) = 20m/s*t

Where t is our variable, time in seconds.

Now, at t = 5s, the car starts accelerating.

Ac(t) = 2m/s^2                    for( t ≥ 5s)

For the velocity of the car, we must integrate that.

V(t) = (2m/s^2)*(t - 5)           for (t ≥ 5s)

Where i introduced a little change in the variable because the velocity of the car starts to increase for t larger than 5 seconds.

For the position of the car we integrate again.

C(t) = (1m/s)*(t - 5)^2            for (t ≥ 5s)

Now, let's answer the questions:

Determine the time at which the speed of the truck is equal to the speed of the police car.

Then we must have:

V(t) = (2m/s^2)*(t - 5)  = 20m/s.   (Remember that we only can use times requal or larger than 5 seconds).        

2m/s^2*t - 10m/s = 20m/s

2m/s^2*t = 30m/s

t = (30/2) s = 15s

The velocities of both vehicles will be the same after 15 seconds.

t1 = 15s

How the positions will compare at this time?

The easier thing will be to evaluate the position equation of each vehicle in this time:

T(15s) = 20m/s*15s = 300m

C(15s) = (1m/s^2)*(15s - 5s)^2 = (1m/s^2)*(10s)^2 = 100m.

Then we can see that the truck is 200m ahead of the car.

But remember that the police car is accelerating, so the velocity will keep increasing meaning that eventually, the car will catch the truck.


Related Questions

Which words help you to determine the meaning of the word decelerate in paragraph 3

Answers

Answer:

the words

Explanation:

Answer:

Pressing the brake pedal

Explanation:

Decelerate sounds a lot like the word accelerate, but we know that the speed is decreasing, so it would have to be going down, getting slower, so whichever sounds like a good example of speed decreasing should be a good answer!

Define what velocity means.

Answers

Answer:

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion (e.g. 60 km/h to the north).

List out Units For: Acceleration

Answers

Acceleration units : M/s squared

Unit for Acceleration is m/s² or ms raised to -2

The photo shows dew drops that formed on the grass when temperatures
cooled during the night. Which change of state happened to form the dew?
A. Liquid to gas
B. Gas to liquid
C. Solid to gas
D. Gas to solid

Answers

Gas to a liquid
This is because of condensation
gas to liquid is the answer

1 point
1)A 1 kg brick is carried to up the Eiffel Tower to the 275 m platform. How
much gravitational potential energy does it acquire?

Answers

Answer:

The gravitational potential energy is 2,750 Joules

Explanation:

Given the following data;

Mass of brick = 1kg

Height of Eiffel Tower = 275m

Potential energy can be defined as the energy possessed by an object due to its position.

Mathematically, potential energy is;

[tex] P = mgh[/tex]

Also, we know acceleration due to gravity = 10m/s2

[tex] P = mgh[/tex]

[tex] P = 1 * 275 * 10 [/tex]

P = 2750 Joules.

Hence, the gravitational potential energy the brick acquired is 2750 Joules.

Dos pilotos suicidas, que están inicialmente a una distancia de 500 m entre sí, deciden chocar directamente de frente arrancando ambos desde el reposo. Ambos autos pueden desarrollar una aceleración máxima constante de 15 m/s2 . Si el piloto A arranca un segundo antes que el piloto B, encuentra: a) la posición donde los autos chocan, medida a partir de la posición donde arranca el piloto A, y b) la rapidez relativa de la colisión (la rapidez de B con respecto a A justo antes de la colisión, ó viceversa).

Answers

Answer:

a) El punto de colisión de los dos automóviles desde donde parte el conductor del automóvil A es de aproximadamente 293,14 metros.

b) La velocidad del automóvil A, en relación con la velocidad del automóvil B, es de 15 m / s

Explanation:

Los parámetros del movimiento son;

La distancia entre ambos coches = 500 m

La aceleración de ambos coches = 15 m / s²

La dirección de movimiento de ambos coches = uno hacia el otro

La hora de inicio del conductor A = Un segundo antes de la hora de inicio del conductor B

Por lo tanto, de la ecuación de movimiento, tenemos;

s = u · t + 1/2 · a · t²

v² = u² + 2 · a · s

Dónde;

u = La velocidad inicial de los autos = 0 (los autos parten del reposo)

t = El tiempo de movimiento de una aceleración dada

a = La aceleración = 15 m / s²

s = La distancia recorrida en el tiempo t

Por lo tanto, para el controlador A, tenemos;

s₁ = 0 × (t + 1) + 1/2 × 15 × (t + 1) ² = 7.5 × (t + 1) ²

s₁ = 7.5 × (t + 1) ²

Para el conductor B, tenemos;

s₂ = 0 × t + 1/2 × 15 × t² = 7.5 × t²

s₂ = 7,5 × t²

Dado que ambos chocan a lo largo del camino de 500 m, tenemos;

s₁ + s₂ = 500 metros

∴ 7.5 × (t + 1) ² + 7.5 × t² = 500

∵ s₁ + s₂ = 7.5 × (t + 1) ² + 7.5 × t²

Lo que da;

15 · t² + 15 · t + 7.5 = 500

15 · t² + 15 · t - 492,5 = 0

Resolver usando la aplicación en línea da; t = -6,25181 o t = 5,25181

Dado que t es un número natural, tenemos el valor correcto para t = 5.25181 segundos

a) Por tanto, el punto de colisión de los dos coches desde donde parte el conductor del coche A es;

s₁ = 7.5 × (t + 1) ² = 7.5 × (5.25181 + 1) ² ≈ 293.14 metros

El punto de colisión de los dos automóviles desde donde parte el conductor del automóvil A ≈ 293,14 metros

b) La semilla de A en el punto de colisión se da de la siguiente manera

Velocidad, v₁ = u + a × (t + 1) = 0 + 15 × (5.25181 + 1) ≈ 93.78

v₁ ≈ 93,78 m / s

La semilla de B en el punto de colisión también se da de la siguiente manera

Velocidad, v = u + a × (t) = 0 + 15 × 5.25181 ≈ 78.78

v₁ ≈ 78,78 m / s

Por lo tanto, la velocidad del automóvil A, en relación con la velocidad del automóvil B, [tex]v_{relative}[/tex] se da como sigue;

 = v₁ - v₂ = 93,78 m / s - 78,78 m / s = 15 m / s

la velocidad del automóvil A, relativa a la velocidad del automóvil B = 15 m/s.

What the meaning of centerpiece​

Answers

Answer:

1 : an object occupying a central position especially : an adornment in the center of a table. 2 : one that is of central importance or interest in a larger whole the centerpiece of a political agenda.

Explanation:

What is an centerpiece?
Answer is :
It is an ornament or display placed in the middle of a dining table
It’s also a (noun)

#7 If the Moon’s mass was suddenly tripled, what would occur to the gravitational force between the Earth and the Moon?
(A) Gravitational force would increase by a factor of 3.
(B) Gravitational force would decrease by a factor of 3.
(C) Gravitational force would increase by a factor of 9.
(D) Gravitational force would decrease by a factor of 9.

Answers

Answer:

well it would be (A) Gravitational force would increase by a factor of 3.

Explanation:

because the moon is the only thing that gained mass not the Earth

If an object is moving with constant acceleration, its velocity must

a
change by varying amounts depending on its speed.
b
always decrease.
c
be constant also.
d
change by the same amount each second.

Answers

change by the same amount each second. i think

how much force is needed to accelerate 300 kg at a rate of 4 m/s/s​

Answers

Answer:

1200

Explanation:

Force = Mass x Acceleration

Answer:

[tex]\boxed {\tt 1,200 \ Newtons }[/tex]

Explanation:

Force can be found by multiplying the mass by the acceleration.

[tex]F=m*a[/tex]

The mass is 300 kilograms.

The acceleration is 4 meters per second squared.

[tex]m= 300 \ kg\\a= 4 \ m/s^2[/tex]

Substitute the values into the formula.

[tex]F= 300 \ kg * 4 \ m/s^2[/tex]

Multiply.

[tex]F= 1200 \ kg * m/s^2[/tex]

1 Newton is equal to 1 kilograms meters per second squared, so our current answer of 1200 kg m/s² is equal to 1200 Newtons.

[tex]F= 1200 \ N[/tex]

The force needed is 1,200 Newtons.

An ant is crawling along a yardstick that is pointed with the 0-inch mark to the east and the 36-inch mark to the west. It starts at the 14-inch mark, crawls to the 20-inch mark, then moves to the 16-inch mark. What was the total distance the ant traveled?

Answers

Given :

An ant is crawling along a yardstick that is pointed with the 0-inch mark to the east and the 36-inch mark to the west.

It starts at the 14-inch mark, crawls to the 20-inch mark, then moves to the 16-inch mark.

To Find :

The total distance the ant traveled.

Solution :

Total distance travelled by ant = (distance between 14 and 20 inch mark) +

                                                      (distance between 20 and 16 inch mark)

Total distance = (20-14 ) + ( 20-16) = 6 + 4 = 10 inch.

Therefore, total distance the ant traveled is 10 inch.

Hence, this is the required solution.

A toy car rolls down a hill starting from rest. After 4.2 seconds its velocity is 18 meters per second. What is the acceleration of the car ?

SOMEONE PLZ HELP :(
WILL MARK BRAILIEST

Answers

Answer: if this is the same question I think it’s 24

Explanation:

How are velocity, wavelength, and frequency related

Answers

Answer:

The wave velocity and the wavelength are related to the wave's frequency and period by vw=λT or vw=fλ. The time for one complete wave cycle is the period T. The number of waves per unit time is the frequency ƒ. The wave frequency and the period are inversely related to one another.

Explanation:

Question 4 of 20
Luke wraps a magnetized steel nail with several coils of insulated wire and
then connects the loose ends of the wire to a 10 W lightbulb. Which step
could he take next to get the lightbulb to light up?
O A. Replace the magnetized nail with a nonmagnetic metal to cause
an electric current to flow in the wire.
O B. Remove the magnetized nail from the wire coil to induce a
magnetic field that will flow through the wire.
C. Move the magnetized nail back and forth within the wire coil to
induce an electric current in the wire.
D. Add several more coils of the wire around the magnetized nail to
make a stronger electric current.
SUBMIT

Answers

Answer:

C. Move the magnetized nail back and forth within the wire coil to induce an electric current in the wire.

Hope this helps.

please help
Which equipment is best to hold and to measure liquids?
A). flask and graduated cylinder
B). scale and ruler
C). caliper and thermometer
D). stopwatch and beaker

Answers

Answer:

I'm pretty sure that the answer is A

How do electromagnetic waves affect you?

Answers

Answer:

At low frequencies, external electric and magnetic fields induce small circulating currents within the body. ... The main effect of radiofrequency electromagnetic fields is heating of body tissues. There is no doubt that short-term exposure to very high levels of electromagnetic fields can be harmful to health.

Why does sonar use ultrasound rather than sound?

Answers

Answer;  Ultrasonic waves (sounds having frequency greater than 20,000 Hz) are used in sonar because: ... Ultrasonic waves can penetrate water to long distances (because of their high frequency and very short wavelength), but ordinary sound waves or infrasonic waves cannot penetrate water to such long distances.

Answer:

Ultrasonic waves (sounds having frequency greater than 20,000 Hz) are used in sonar because: ... Ultrasonic waves can penetrate water to long distances (because of their high frequency and very short wavelength), but ordinary sound waves or infrasonic waves cannot penetrate water to such long distances

Explanation:

What will be acceleration due to gravity of a feather and coin if
they are dropped in vacuum?​

Answers

Explanation:

Hey there!

We know that the objects in vacuum falls equally on the surface or bottom. As there is no air resistance in vacuum, the objects has equal stabdard acceleration. (i.e g = 9.8m/s^2)

So, the acceleration due to gravity is 9.8m/s^2.

Hope it helps....

A runner moves at an average speed of 3.0 m/s and covers 9.5 km. In seconds, how long does the run take?

28.5 s
29.0 s
3.16 s
3200 s

Answers

Answer:

3200 seconds

Explanation:

If he ran at 3 m/s for 28.5 seconds, he would have run 85.5 meters

29 seconds would be 87 meters run not 9.5 km

3200 s is the right answer

Protons are found only in the atomic nucleus.
TRUE
FALSE

Answers

Answer:

true

Explanation:

Protons and neutrons are found in the nucleus

Biomes on Earth have exhibited changes throughout history that have been caused by a variety of factors. Over the past 50 years, the amount of tropical rainforest acreage found throughout the world has decreased from 14.8 billion acres to 8.6 billion acres due to deforestation. What factor is likely most responsible for the changes observed in the world's rainforests? a. volcanic activity b. human activity c. temperature changes d. solar eclipses Please select the best answer from the choices provided A B C D

Answers

Answer:

b

Explanation:

The factor that is most likely to be responsible for the changes observed in the world's rainforest is human activities.

There has been a surge in the human population leading to an increased need for housing, foods, and other infrastructures. All these needs are directly or indirectly provided by the forest. Hence, the more the population of human expands, the more pressure that would be exerted on the rainforest and, indeed, other forests of the world.

The correct option is b.

which one of the following is a derived Si unit a. Newton, b. Meter, c. Mole, d. Kiogram

Answers

Answer:

The SI is founded on seven SI base units for seven base quantities assumed to ... The SI derived units for these derived quantities are obtained from these ... mass density, kilogram per cubic meter, kg/m3 ... amount-of-substance concentration, mole per cubic meter, mol/m3 ... solid angle, steradian (a), sr (c), -, m2·m-2 = 1 (b).

Kilogram is a derived SI unit of the following.

Thus, A universal standard for expressing the magnitudes or quantities of significant natural events is the International System of Units.

The acronym SI, which derives from the French term Systèm international  stands for the System of Units, also known as the metric system. The meter-kilogram-second (MKS) system, an earlier unit of measurement, serves as the foundation for the SI standard.

The SI standard is promoted and explained by the Bureau international des poids et mesures (BIPM). The organization was founded in 1875 and is known as the International Bureau of Weights and Measures in English. It is governed by the International Committee for Weights and Measures (CIPM).

Thus, Kilogram is a derived SI unit of the following.

Learn more about Kilogram, refer to the link:
https://brainly.com/question/29761698

#SPJ2

Which image shows an example of the electromagnetic force in action?

Answers

Answer:

the answer is A the one that has the green ball as particles

Explanation:

The second image showing an electromagnet is an example of the electromagnetic force in action therefore the correct option is B

What is electromagnetic force?

It is a type of force that occur between electrically charged particles. The electromagnetic force is the combination of all the electrical and magnetic forces generated from any charged particle,

These electromagnetic forces either be attractive or repulsive.

The force generated from a simple bar magnet is an example of the electromagnative force, hence the correct option is B

Learn more about electromagnetic forces

https://brainly.com/question/13191643

#SPJ5

Which model of the atom has electrons traveling in specific paths around the nucleus? Bohr's model Rutherford's model Thomson's model Dalton's model

Answers

Answer:

A, Bohr's model

Explanation:

Took the quiz, hope it's right for you.

(The other three did have something to do with it they just didn't create that specific model)

The model of the atom that has electrons traveling in specific paths around the nucleus is Rutherford's model.

Therefore, the correct answer is option B

J. J Thomson proposed that the atom is a sphere of positively charged matter in which negatively charged electron are embedded.

In Rutherford's model of atomic structure, the electrons moves in orbits by electrostatic attraction to the positively charged nucleus.

According to Dalton's atomic theory, atom were indestructible and indivisible  solid particle.

Bohr's model made assumption that electron can only exist in circular orbits of definite quantum energy.  

According to the question, the model of the atom that has electrons traveling in specific paths around the nucleus is Rutherford's model.

Therefore, the correct answer is option B

Learn more here : https://brainly.com/question/16776207

Classify each of the following chemical reactions. Upper S plus upper O Subscript 2 right arrow upper S upper O subscript 2. Upper C a upper C l subscript 2 plus 2 upper A g upper N upper O subscript 3 right arrow upper C a (upper n upper O subscript 3) subscript 2 plus 2 upper A g upper C l. Upper Z n plus upper C u upper S upper O subscript 4 right arrow upper C u plus upper Z n upper S upper O subscript 4. 2 upper N a subscript 2 upper O right arrow 4 upper N a plus upper O subscript 2.

Answers

Answer:

synthesis and combustion

double replacement

single replacement

decomposition only

in that exact order edge 2020

The presented reactions are:

S + O₂ ⇒ SO₂    Synthesis or combination

CaCl₂ + AgNO₃ = Ca(NO₃)₂ + 2 AgCl   Double displacement

Zn + CuSO₄ = Cu + ZnSO₄   Single displacement

2 Na₂O = 4 Na + O₂   Decomposition

Let's consider and classify the following reactions.

S + O₂ ⇒ SO₂

This is a synthesis or combination reaction. 2 compounds combine to form another.

CaCl₂ + AgNO₃ = Ca(NO₃)₂ + 2 AgCl

This is a double displacement reaction. Both compounds exchange their cations and anions.

Zn + CuSO₄ = Cu + ZnSO₄

This is a single displacement reaction. A metal displaces other metal from its salt.

2 Na₂O = 4 Na + O₂

This is a decomposition reaction. A compound decomposes into 2 other compounds.

The presented reactions are:

S + O₂ ⇒ SO₂    Synthesis or combination

CaCl₂ + AgNO₃ = Ca(NO₃)₂ + 2 AgCl   Double displacement

Zn + CuSO₄ = Cu + ZnSO₄   Single displacement

2 Na₂O = 4 Na + O₂   Decomposition

Learn more: https://brainly.com/question/21392527

what does the galaxy made of ?​

Answers

Galaxies are sprawling systems of dust, gas, dark matter, and anywhere from a million to a trillion stars that are held together by gravity. Nearly all large galaxies are thought to also contain supermassive black holes at their centers.

A force of 75 N at an angle of 15° to the direction of motion moves a chair 3 m. Which change would result in more work being done on the chair?

Answers

Answer:

Decreasing the angle to 10

Explanation:

Edge 2020

An space probe built on Earth has a mass of 750 kg. Calculate the weight of the space probe on Earth.

Answers

Answer:

7357.5N

Explanation:

Weight is the force used to pull a mass of object towards the centre of the Earth. The force is 9.81 N/kg.

so, Weight = mass × 9.81

the weight of the space probe should be: 750 × 9.81 = 7357.5 N

Answer:

7350N

Explanation:

Data

m-750kg

g-9.8

W=mg

=750 x 9.8

=7350N

Eclipses occur because the Moon?
A
does not create its own light and only reflects light from the Sun.
o
does not create its own light and only reflects the light from Earth.
o
с
creates its own light, which is blocked by the Sun during an eclipse.
creates its own light, which is blocked by Earth during an eclipse.

Answers

I’m just here typing don’t mind me

Answer:

с

creates its own light, which is blocked by the Sun during an eclipse.

Explanation:

might not be right but its what i remember

It is your parent's 25th Wedding Anniversary and you thought it would be special to throw them a surprise party. Your entire family is up north at your Traverse City cottage (240 miles from your home) and you plan on waking up early Saturday morning to drive home and set up for the party. You wake up at 10:00 am to head out but to your surprise your parents decide on leaving at 11:00 am instead of 1:00 pm like they originally planned. Your father ALWAYS drives 60 miles per hour on the expressway and it will take you about 2 hours to set up for the party. How fast must you drive in order to get home in enough time to make the surprise a success? Show your work.

Answers

Answer:

120 miles per hour.

Explanation:

We need to find the time it takes my parents to drive home from the cottage. Since my father drives at 60 miles per hour, and the cottage is 240 miles from our home, and distance = speed × time. So, time = distance/speed = 240 mi/60 mi/h = 4 h.

So, it will take my father 4 hours to drive home from the cottage.

Since I have 2 hours to prepare for the party, the time left for me to drive to the cottage is 4 - 2 hrs = 2 hrs.

So, I'm supposed to drive to the cottage in at most 2 hours.

The speed at which I must drive in this time period is thus,  speed = distance/time = 240 miles/2 hours = 120 miles per hour.

So, I must drive at a minimum speed of 120 miles per hour.

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What are the common nouns in this sentence:Kelly told me about a big sale at Toy City on Dodge Street. What city is furthest southwest in Europe? The hypoxic zone in the Gulf of Mexico is not unique; at least 200 dead zones exist at estuaries and along seacoasts worldwide. These low-oxygen regions share many of the same causes, and they all have ecological and economic repercussions for ecosystems and people. Fortunately, we can pursue strategies to lessen the number, severity, and impacts of dead zones. The following list includes examples of factors that contribute to the development of dead zones (the cause), the consequences that result from dead zones, and possible solutions. Which of the following are consequences of dead zones?a. Economic losses for fisher's b. Death or aquatic organism that cannot escape c. Policies to promote no-till agriculture d. Construction of wetlands to absorb nutrients e. Nutrient runoff from agriculture fertilizers, manure, and urban sources, which leads to rapid algal growth and subsequent bacterial decomposition what is a unit of electrical flow called What are the advantages and disadvantages of owning versus outsourcing for each of these components (staff, computer servers, software licensing, and data storage)? Find the distance between each pair of points in the coordinate plane.(3,-2) and (2,-1) who does gymnastics?answer if you do only write a poem or song on the topic of our identity which of the following is considered a condition of the nervous system and not a disease of the nervous system?celebral palsyepilepsymultiple sclerosisparkinson's i need help can yall help Which connection would be considered a text-to-world connection?connecting the plot of a novel about the American Revolution with modern day eventsconnecting a villain in a short story with other antagonists in novels connecting a biography of a revolutionary leader with an article about the Mexican Revolutionconnecting the theme of an adventure novel with a theme of a fantasy novel plssssssssssssssssssssssss help for testYour math class is collecting canned food for a local food drive. The goal is to collect at least 130 cans but no more than 250 cans due to space limitations. There are 24 students in your math class and your teacher has promised to bring in 10 cans. Select which inequalities represent the possible numbers n of cans that each student should bring in. 3.A normal bus carries x passengers.A large bus will carry twice as many passengers than the normal busA small bus will carry 8 passengers less than the normal bus.Altogether the buses carry 128 passengers.(a) Form a simplified equation in terms of x There were five bees in a hive how many more bees need to go in the high for there to be 14 bees PLSSSS HELLPPPP MEEEEEEE ASAPPPP I WIILL GIVE BRAINLIEST!!!!!!!!! PLS SHOW WORK STEP BY STEP Please help me with this problem g you are eligible for a 30 year fixed rate home mortgage with 3.6% interest rate what is the maximum loan you can get The two major immigration stations in the United States were locatedin San Francisco in the West and New York in the East.in Philadelphia in the East and Chicago in the Midwest.in New York in the North and Charleston in the South.O in San Francisco in the West and Philadelphia in the East. Which statement accurately describes impulse?State corrrect ans What did the Persians use to purchase goods in their empire?1. bartering2. sea shells3. salt4. coins