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
just olya [345]
3 years ago
5

An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in

cm and t in seconds. Give decimal answers below. (a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second? (b) What is t the first time that the object is at its farthest right? (c) At the time found in part (b), what is the object's velocity? (d) At the time found in part (b), what is the object's acceleration?
Physics
1 answer:
CaHeK987 [17]3 years ago
8 0

Answer:

a.) 10Hz

b.) 0.1 s

c.) 187.4 m/s

d.) -412.6 m/s^2

Explanation:

Given that an object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. Give decimal answers below.

(a) How many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second?

from the equation given,  the angular speed w = 20π

but w = 2πf

where f = frequency.

substitute w for 20π

20π = 2πf

f = 20π/2π

f = 10 Hz

(b) What is t the first time that the object is at its farthest right?

since F = 1/T

T = 1 / f

T = 1/10

T = 0.1 s

Therefore, the t of  first time that the object is at its farthest right is 0.1 s

(c) At the time found in part (b), what is the object's velocity?

The velocity can be found by differentiating the equation;

x(t) = 3sin(20πt)

dx/dt = 60πcos(20πt)

where dx/dt  = velocity V

V = 60πcos(20π * 0.1)

V = 187.4 m/s

(d) At the time found in part (b), what is the object's acceleration?

to get the acceleration, differentiate equation  V = 60πcos(20πt)

dv/dt = -1200πSin(20πt)

dv/dt = acceleration a

a = -1200πSin(20πt)

substitute t into the equation

a = -1200πSin(20π * 0.1)

a = - 412.6 m/s^2

You might be interested in
The place kicker on a football team kicks a ball from ground level with an initial speed of 4.00 m/s at an angle of 29.0° above
mafiozo [28]

Answer:

0.4 s

Explanation:

The time that the ball is in the air can be found with the next formula:

time = t = \frac{2v_{o}sen\beta}{g}

where v_{o} is the initial velocity of the ball, in this case:

v_{o}=4.00 m/s

β is the angle: β = 29.0°

And g is the acceleration of gravity: g=9.81m/s^2

Replacing all the values to find t, we have:

time = t = \frac{2(4m/s)sen(29)}{9.81m/s^2} = 0.4s

Thus, the ball is 0.4s in the air.

3 0
3 years ago
) The magnitude of scalar product of two unit vectors perpendicular to each other is ​
fenix001 [56]

This question involves the concept of the scalar product.

The magnitude of the scalar product will be "0".

<h3>SCALAR PRODUCT</h3>

The scalar product, also known as the dot product of the two vectors is given by the following formula:

A.B = |A||B|Cos\theta

where,

  • A.B = Scalar product = ?
  • |A| = Mangnitude of vector A = 1 unit
  • |B| = Magnitude of Vector B = 1 unit
  • θ = Angle between vectors = 90°

Therefore,

A.B = (1)(1)Cos90^o = (1)(1)(0)

A.B = 0

Learn more about scalar product here:

brainly.com/question/6849226

5 0
2 years ago
It takes 24 hours for _______?
tigry1 [53]

Answer:

C

Explanation:

Earth rotates once in about 24 hours with respect to the Sun, but once every 23 hours, 56 minutes, and 4 seconds with respect to other, distant, stars. Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation.

8 0
3 years ago
A person wants to lose weight by "pumping iron". The person lifts an 80 kg weight 1 meter. How many times must this weight be li
statuscvo [17]

Answer:

37357 sec  

or 622 min

or 10.4 hrs

Explanation:

GIVEN DATA:

Lifting weight 80 kg

1 cal = 4184 J

from information given in question we have

one lb fat consist of 3500 calories = 3500 x 4184 J

= 14.644 x 10^6 J  

Energy burns in 1 lift = m g h

                                  = 80 x 9.8 x 1 = 784 J

lifts required = \frac{(14.644 x 10^6)}{784}

                      = 18679

from the question,

1 lift in 2 sec.

so, total time = 18679 x 2 = 37357 sec  

or 622 min

or 10.4 hrs

3 0
3 years ago
Which of the following statements is true?
erastova [34]

Hi there!

Question - Which of the following statements is true?

Answer - C. You are exposed to nuclear radiation every day.

Why - "radiation in the form of elementary particles emitted by an atomic nucleus, as alpha rays or gamma rays, produced by decay of radioactive substances or by nuclear fission."

6 0
3 years ago
Other questions:
  • Which of the following is created when the ice of a comet starts to melt into gases?
    12·1 answer
  • The rear window in a car is approximately a rectangle, 1.3 m wide and 0.30 m high. The inside rear-view mirror is 0.50 m from th
    15·1 answer
  • A runaway train with a mass of 6,251 kg is approaching the end of the line at a speed of 27 m/s. The end of the line has a massi
    8·1 answer
  • How many meters in 32 kilometers
    6·2 answers
  • If calculated from the traditional date of bith of christ, a decade, a century and milinnium contain a period of...
    10·1 answer
  • Surface currents are driven by _____.<br> wind<br> density<br> salinity<br> temperature
    5·2 answers
  • In interpersonal attraction, the phrase “Birds of a feather flock together” is more accurate than “Opposites attract.”
    10·2 answers
  • Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star.
    14·1 answer
  • The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the part
    8·1 answer
  • What is gram used to measure <br><br> A. volume<br> B. Mass<br> C. distance<br> D. Time
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!