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
Answer:
In a vacuum
Explanation:
Sound is a type of mechanical waves. Mechanical waves are waves that propagate through the oscillation of the particles in a medium, which can be either gas, liquid or solid.
A sound wave in air, for instance, is simply produced by the oscillations of the air particles back and forth along the direction of motion of the wave.
Given this definition, it is clear that mechanical waves (and so, sound waves as well) cannot be transmitted if there is no medium: therefore, they cannot be transmitted in a vacuum. So, the sound of the ringing bell would not be present in a vacuum.
Answer:
the balloon is filled with the 8.5 litre of helium. temperature is 294 kelvin.
party starts at 4 p.m.
the temperature rises 305 kelvin.
the new volume = 4 litres
The answer is:
1. Cure disease
2. Improve livelihoods
3. Understand nature and themselves.
1. Disease has plagued humans since the first man. Therefore, man has always used science to seek a cure for any emerging disease such as cancer today
2. Humans use science to improve livelihoods such as means of faster traveling and increasing yields in the fields
3. Science has been used to understand humans and the environment in which they live. This is evident with the numerous scientific probes that explore the earth and space collecting and analyzing data.
