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
puteri [66]
2 years ago
11

An object moves along the x-axis. Its position is given by the equation y( X = 4t^2 - 41t+ 78 \). Find the position of the

Physics
1 answer:
prohojiy [21]2 years ago
7 0

The object changes direction when its velocity changes sign. You can get the velocity function by differentiating the position function with respect to time <em>t</em> :

<em>x(t)</em> = 4<em>t</em> ² - 41<em>t</em> + 78

→   <em>v(t)</em> = d<em>x(t)</em>/d<em>t</em> = 8<em>t</em> - 41

Solve <em>v(t)</em> = 0:

8<em>t</em> - 41 = 0

8<em>t</em> = 41

<em>t</em> = 41/8 = 5.125

Just to confirm that the velocity indeed changes sign:

• Pick any time before this one to check the sign of <em>v</em> :

<em>v</em> (0) = 8•0 - 41 = -41 < 0

• Pick any time after and check the sign again:

<em>v</em> (6) = 8•6 - 41 = 7 > 0

Now just find the position at this time:

<em>x</em> (5.125) = -433/16 = -27.0625

which means the object is 27.0625 units on the negative <em>x</em>-axis.

You can also do this without calculus by completing the square in the position function:

4<em>t</em> ² - 41<em>t</em> + 78 = 4 (<em>t</em> ² - 41/4 <em>t</em> ) + 78

… = 4 (<em>t</em> ² - 2• 41/8 <em>t</em> + (41/8)² - (41/8)²) + 78

… = 4 (<em>t</em> ² - 2• 41/8 <em>t</em> + (41/8)²) - 4•1681/64 + 78

… = 4 (<em>t</em> - 41/8)² - 433/16

which describes a parabola that opens upward. When <em>t</em> = 41/8 = 5.125, the quadratic term vanishes and the turning point of the parabola occurs at a position of -433/16 units.

You might be interested in
Draw the distance time graph for a body at rest​
Semenov [28]

I hope it is helpful for you...

8 0
3 years ago
Read 2 more answers
How did tycho brahe's model of the universe differ from the greek geocentric model?
SCORPION-xisa [38]
Idkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
4 0
3 years ago
An object has a kinetic energy of 275 j and a momentum of magnitude 25.0 kg · m/s. find the (a) speed and (b) mass of the object
Sergeu [11.5K]
Kinetic energy = momentum^2 / 2 x mass
Mass = (momentum^2/ Kinetic energy) / 2

Mass =  (25^2 / 275) / 2
Mass = 1.136 kg.

momentum = mass x velocity

velocity = mass / momentum
velocity = 1.136 / 25
velocity = 0.04544 m/s
8 0
3 years ago
Read 2 more answers
The International Space Station has a mass of 1.8 × 105 kg. A 70.0-kg astronaut inside the station pushes off one wall of the st
Aleonysh [2.5K]

Answer:

a = 5.83 \times 10^{-4} m/s^2

Explanation:

Since the system is in international space station

so here we can say that net force on the system is zero here

so Force by the astronaut on the space station = Force due to space station on boy

so here we know that

mass of boy = 70 kg

acceleration of boy = 1.50 m/s^2

now we know that

F = ma

F = 70(1.50) = 105 N

now for the space station will be same as above force

F = ma

105 = 1.8 \times 10^5 (a)

a = \frac{105}{1.8 \times 10^5}

a = 5.83 \times 10^{-4} m/s^2

3 0
3 years ago
1. A heat lamp is designed to keep food and other things warm. Would it also make a good tanning lamp? Why or why not?
NemiM [27]
1. becuase it is so hot that it could tan or be used to keep warm.
4 0
3 years ago
Read 2 more answers
Other questions:
  • 5. Describe the relationship between frequency and wavelength.
    11·2 answers
  • The speed of all electromagnetic waves in empty space is 3.00 × 108 m/s. what is the wavelength of radio waves emitted at 83.6 m
    13·1 answer
  • The world record for a 100 m race is 10.44 m/s. How fast is this in mi/h?
    6·1 answer
  • A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 32.0 cm of an unkno
    5·1 answer
  • 2) Write two examples in which an object undergoes more than one type of motion at the same time.
    13·1 answer
  • A pendulum is made of a small sphere of mass 0.250 kg attached to a lightweight string 1.20 m in length. As the pendulum swings
    14·1 answer
  • A charge enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc
    14·1 answer
  • Calculate the amount of heat needed to raise 1.0 kg of ice at -20 degrees Celsius to steam at 120 degree Celsius
    5·1 answer
  • Which statement best describes what happens during a solar eclipse?
    13·2 answers
  • Can someone answer these question for me?​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!