1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitry [639]
3 years ago
10

When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 is extremely w

ell modeled by the simple equation v2x=2Pmt where P=3.6104W is the car's power output, m = 1200kg is its mass, and vx is in m/s. That is, the square of the car's velocity increases linearly with time.
a) What is the car's speed at t=11 s ?

b) What is the car's speed at t=18 s ?

c)Find a symbolic expression, in terms of P, m, and t, for the car's acceleration at time t.

d)Evaluate the acceleration at t=1.0 s .

e) Evaluate the acceleration at t=10 s .
Physics
1 answer:
tigry1 [53]3 years ago
8 0

Answer:

a-)v_{x} = 25.69 m/s

b-)v_{x} = 32.86 m/s

c-)a = \frac{\sqrt{ \frac{2P}{m}}}{ 2\sqrt{t}}}\\

d-)a= 3.87 m/s^{2}

e-)a= 1.22 m/s^{2}

Explanation:

First, lay out the given data:

P = 3.6 x 10^4 W

m=1200 kg

v_{x} ^{2}=\frac{2P}{m}t\\v_{x} ^{2}=\frac{2*3.6*10^{4}}{1200} *t

a)What is the car's speed at t=11 s ?

v_{x}^{2}=\frac{2*3.6*10^{4}}{1200} *t\\v_{x}=\sqrt{60*11} \\v_{x} = 25.69 m/s

b) What is the car's speed at t=18 s ?

v_{x}^{2}=\frac{2*3.6*10^{4}}{1200} *t\\v_{x}=\sqrt{60*18} \\v_{x} = 32.86 m/s

c) Find a symbolic expression, in terms of P, m, and t, for the car's acceleration at time t.

An expression for the acceleration can be defined by finding the derivative of the velocity equation:

v_{x} =\sqrt{ \frac{2P}{m}t}\\\frac{d(v_{x})}{dt} = \frac{d}{dt}(\sqrt{ \frac{2P}{m}t})\\\frac{d(v_{x})}{dt} = \frac{d}{dt}(\sqrt{ \frac{2P}{m}}*t^{\frac{1}{2}} )\\\frac{d(v_{x})}{dt} = (\sqrt{ \frac{2P}{m}}* \frac{1}{2}t^{\frac{-1}{2}} )\\\\\frac{d(v_{x})}{dt} = \frac{\sqrt{ \frac{2P}{m}}}{ 2\sqrt{t}}}\\a = \frac{\sqrt{ \frac{2P}{m}}}{ 2\sqrt{t}}}\\

d) Evaluate the acceleration at t=1.0 s

a = \frac{\sqrt{ \frac{2P}{m}}}{ 2\sqrt{t}}}\\\\a = \frac{\sqrt{ \frac{2*3.6*10^{4}}{1200}}}{ 2\sqrt{1}}}\\\\a= 3.87 m/s^{2}

e) Evaluate the acceleration at t=10 s

a = \frac{\sqrt{ \frac{2P}{m}}}{ 2\sqrt{t}}}\\\\a = \frac{\sqrt{ \frac{2*3.6*10^{4}}{1200}}}{ 2\sqrt{10}}}\\\\a= 1.22 m/s^{2}

You might be interested in
A rock falls off a cliff. How fast is the rock traveling vertically two seconds later?
Vikentia [17]
The rock it traveling really, really fast.
It is hard to exactly determine how fast bc u need the height of the cliff and how big the rock is.
Hope this helps and can I get brainliest answer!
8 0
3 years ago
An atom is.......Help?
Dmitry_Shevchenko [17]
The smallest level of ordination in living things. Every living thing is made up of atoms. Atoms are made up of protons, neutrons, and electrons.
5 0
3 years ago
A storage tank containing oil (SG=0.92) is 10.0 meters high and 16.0 meters in diameter. The tank is closed, but the amount of o
blagie [28]

Answer:

a-1 Graph is attached. The relation is linear.

a-2 The corresponding height for 68 kPa Pressure is 7.54 m

a-3 The corresponding weight for 68 kPa Pressure is 1394726kg

b The original height of the column is 5.98 m

Explanation:

Part a

a-1

The graph is attached with the solution. The relation is linear as indicated by the line.

a-2

By the equation

P=\rho \times g \times h

Here

  • P is the pressure which is given as 68 kPa.
  • ρ is the density of the oil whose SG is 0.92. It is calculated as

                                       \rho=S.G \times \rho_{water}\\\rho=0.92 \times 1000 kg/m^3\\\rho=920 kg/m^3\\

  • g is the gravitational constant whose value is 9.8 m/s^2
  • h is the height which is to be calculated

                                        P=\rho \times g \times h\\h=\frac{P}{\rho \times g}\\h=\frac{68 \times 10^3}{920 \times 9.8}\\h=7.54m

So the height of column is 7.54m

a-3

By the relation of volume and density

M=\rho \times V

Here

  • ρ is the density of the oil which is 920 kg/m^3
  • V is the volume of cylinder with diameter 16m calculated as follows

                             V=\pi r^2h\\V=3.14\times (8)^2 \times 7.54\\V=1515.23 m^3

Mass is given as

                             M=\rho \times V\\M=920 \times 1515.23\\M=1394726kg

So the mass of oil leading to 68kPa is 1394726kg

Part b

Pressure variation is given as

                            \Delta P=P_{obs}-P_{atm}\\\Delta P=115-101 kPa\\\Delta P=14 kPa\\

Now corrected pressure is as

P_c=P_g-\Delta P\\P_c=68-14 kPa\\P_c=54 kPa

Finding the value of height for this corrected pressure as

P_c=\rho \times g \times h\\h=\frac{P_c}{\rho \times g}\\h=\frac{54 \times 10^3}{920 \times 9.8}\\h=5.98m

The original height of column is 5.98m

4 0
3 years ago
An unknown material has a mass of 0.447 kg, and its temperature increases by 2.87°C when 943 J of heat are added. What is the sp
Sergeeva-Olga [200]

Answer:

735 J/kg/C

Explanation:

Q = mcT

943 = (0.447)( c )(2.87)

1.28289c = 943

c = <u>7</u><u>3</u><u>5</u><u> </u><u>J</u><u>/</u><u>k</u><u>g</u><u>/</u><u>C</u><u> </u><u>(</u><u>3</u><u> </u><u>s</u><u>f</u><u>)</u>

4 0
3 years ago
In three sentences, please describe SIMPLE HARMONIC motion, and give two examples. Thank you! :-)
11Alexandr11 [23.1K]
A system that repeats to and from its mean or rest point. that executes harmonic motion. a few examples I've heard of are since the springtime a mass-spring system,a swing, simple pendulum, one more example is a steel ball rolling in a curved is this what you need or do you need three more sentences dish. to get S.H.M a body just displaced away from the resting position and of course then is released. the human body oscillates due to the reinforce that pulls it back do you need anything else answered on this and I'll answer it
3 0
3 years ago
Other questions:
  • 1. A container has a mass of 36 kg. How much does the container weigh?
    11·2 answers
  • If a chlorine atom gains or loses a valence electron, it becomes a charged
    6·1 answer
  • The potential difference between two points, A and B, in an electric field is 2.00 volts. The energy required to move a charge o
    5·1 answer
  • __________ is the term for a reaction where energy is released.
    15·1 answer
  • The change in electric potential energy per unit charge is
    9·2 answers
  • A garbage truck has a mass of 2100 kg. It starts from rest and travels 75 meters in 15 seconds. The truck uniformly accelerates
    9·1 answer
  • Why are fossil fuels like coal, oil, and natural gas<br> called nonrenewable resources?
    10·1 answer
  • Two uniform solid spheres of the same size, but different mass, are released from rest simultaneously at the same height on a hi
    14·1 answer
  • A car bounces up and down on its springs at 1.0 Hz with only the driver in the car. Now the driver is joined by four friends. Th
    9·1 answer
  • Which term names the part of a sound wave by which frequency or pitch is measured?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!