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
USPshnik [31]
3 years ago
13

The only force acting on a 3.1 kg body as it moves along the positive x axis has an x component fx = -8x n, where x is in meters

. the velocity of the body at x = 2.0 m is 11 m/s. (a) what is the velocity of the body at x = 4.5 m? (b) at what positive value of x will the body have a velocity of 5.8 m/s?
Physics
1 answer:
My name is Ann [436]3 years ago
4 0
<span>(a) -9.97 m/s
 (b) x = 2.83

   This is a simple problem in integral calculus. You've been given part of the 2nd derivative (acceleration), but not quite. You've been given the force instead. So let's setup a function for acceleration.

   f''(x) = -8x N / 3.1 kg= -8x kg*m/s^2 / 3.1 kg = -2.580645161x m/s^2

   So the acceleration of the body is now expressed as
 f''(x) = -2.580645161x m/s^2

    Let's calculate the anti-derivative from that.
 f''(x) = -2.580645161x m/s^2
 f'(x) = -1.290322581x^2 + C m/s

   Now let's use the known velocity value at x = 2.0 to calculate C
 f'(x) = -1.290322581x^2 + C 1
1 = -1.290322581*2^2 + C
 11 = -1.290322581*4 + C
 11 = -5.161290323 + C
 16.161290323 = C

   So the velocity function is
  f'(x) = -1.290322581x^2 + 16.161290323

   (a) The velocity at x = 4.5
  f'(x) = -1.290322581x^2 + 16.161290323
 f'(4.5) = -1.290322581*4.5^2 + 16.161290323
 f'(4.5) = -1.290322581*20.25 + 16.161290323
  f'(4.5) = -26.12903227 + 16.161290323
 f'(4.5) = -9.967741942

   So the velocity is -9.97 m/s

   (b) we want a velocity of 5.8 m/s
5.8 = -1.290322581x^2 + 16.161290323
 0 = -1.290322581x^2 + 10.36129032
 1.290322581x^2 = 10.36129032
 x^2 = 8.029999998
 x = 2.833725463</span>
You might be interested in
What type of energy is involved when a river moves sediment and erodes its banks?
ziro4ka [17]
<span>First question: The type of energy involved when a river moves sediment and erodes its banks is: option d. Kinetic energy. Kinetic energy is the energy associated with motion. A body (in this case the water) that moves has an energy associated with its motion that is proportional to the speed (exactly to the square of the speed). When the water collides with the banks it is the kinetic energy of the river that erodes it Second question: the answer is the option d. As gravity pulls water down a slope potential energy changes to knietic energy. This is the, water loses altitude and gains velocity. The potential energy. which is proportional to the height, decreases and the kinetic energy, which is proportional to the square of the speed, increases.</span>
8 0
3 years ago
What's the difference between Uniform magnetic field and Non-uniform magnetic field?
Galina-37 [17]
Magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point specified by both direction and a magnitude. So uniform magnetic field has equal amount of force or magnetic force in both side of the object while the non uniform magnetic field has one of the object exert more than the other 
4 0
3 years ago
If the length of a ramp (an inclined plane) is 12 ft, and it rises 2 ft, what is its MA?
dangina [55]
The MA is 6! Hope This Helps!
3 0
3 years ago
1. A diver dives off of a raft - what happens to the diver? The raft? How does this relate to Newton's Third Law?  Action Force:
Natali [406]
The Action Force of this scenario is the pushing force of the Diver. The Reaction Force is the raft pushing back on the diver. 

The Third Law of Motion states that "For every action, there is an equal and opposite reaction." Now when the diver dives off the raft, the raft is also pushing the same amount of force as the diver did as he dives off. The diver will then move forward and the raft on the other hand will move backwards.

The movement of the raft shows the opposite force. It will move backwards depending on how strong the diver will push off on the raft. And the amount of force he pushes on it, the raft will exert the same force so the stronger the force of the diver, the farther he will go because the raft will push him in that same direction as it goes backwards. 
7 0
3 years ago
At a place where an object is thrown vertically downward with a speed of while a different object is thrown vertically upward wi
Bumek [7]

Answer:

Both objects will undergo the same change in velocity

Explanation:

m = Mass of the Earth =  5.972 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

r = Radius of Earth = 6371000 m

m = Mass of object

Any object which is falling has only the acceleration due to gravity.

ma=\dfrac{GMm}{r^2}\\\Rightarrow a=\dfrac{GM}{r^2}\\\Rightarrow a=\dfrac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{(6.371\times 10^6)^2}\\\Rightarrow a=9.81364\ m/s^2

The acceleration due to gravity on Earth is 9.81364 m/s²

So, the speeds of the objects will change at an equal rate of 9.81364 m/s² but the change will be negative when an object is thrown up.

Hence, both objects will undergo the same change in velocity.

4 0
3 years ago
Other questions:
  • If the moon were 2 times closer to earth than it is now, the gravitational force between earth and the moon would be
    12·1 answer
  • Stan and Silvia Waterson go on a vacation and leave their 17 year old daughter, Jessie, in charge of the house and her two young
    5·1 answer
  • Which of the following can influence one???s ability to detect stimuli and increase one???s responsiveness to stimuli in dangero
    13·2 answers
  • As the skydiver falls to Earth, she experiences positive acceleration due to
    12·2 answers
  • Suppose you lift a 20 kg box by a height of 1.0 m.
    15·2 answers
  • If an astronaut weighs 900 n on earth, what does he weigh on the planet venus?
    6·1 answer
  • Mass of Sun
    12·1 answer
  • A soccer player kicks a ball with a force of 900 newtons. The ball has a mass of 0.5 kilograms. At what rate will the ball accel
    12·1 answer
  • A plane mirror forms an image of an object because it ____________ light from the object.
    6·1 answer
  • HELP THIS LAST DAY!!!
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!