Answer:
2.69 m/s
Explanation:
Hi!
First lets find the position of the train as a function of time as seen by the passenger when he arrives to the train station. For this state, the train is at a position x0 given by:
x0 = (1/2)(0.42m/s^2)*(6.4s)^2 = 8.6016 m
So, the position as a function of time is:
xT(t)=(1/2)(0.42m/s^2)t^2 + x0 = (1/2)(0.42m/s^2)t^2 + 8.6016 m
Now, if the passanger is moving at a constant velocity of V, his position as a fucntion of time is given by:
xP(t)=V*t
In order for the passenger to catch the train
xP(t)=xT(t)
(1/2)(0.42m/s^2)t^2 + 8.6016 m = V*t
To solve this equation for t we make use of the quadratic formula, which has real solutions whenever its determinat is grater than zero:
0≤ b^2-4*a*c = V^2 - 4 * ((1/2)(0.42m/s^2)) * 8.6016 m =V^2 - 7.22534(m/s)^2
This equation give us the minimum velocity the passenger must have in order to catch the train:
V^2 - 7.22534(m/s)^2 = 0
V^2 = 7.22534(m/s)^2
V = 2.6879 m/s
The point at which all motion stops.
Answer:
False
Explanation:
In addition to stars, our galaxy contains abundant diffuse matter that is distributed throughout its volume and constitutes what we call the interstellar medium. This medium plays a fundamental role in the life cycle of the stars, since it is where the matter from which they are born resides, and it is the place to which it returns when the stars expel their outer layers at death.
The interstellar medium is a complex environment. <u>Its matter is </u><u>not </u><u>distributed uniformly</u>, but consists of different phases with temperatures ranging from a few degrees Kelvin (near absolute zero) in the areas of star formation to the millions of degrees Kelvin observed in supernova remnants. The densities of interstellar matter also vary orders of magnitude according to the phase, but they are always so low that they rival those that can be achieved in the best vacuum chambers of terrestrial laboratories. Depending on the density and temperature conditions, interstellar matter is in a molecular, atomic, or ionized state, although the state is not permanent, since matter circulates between the different phases in a continuous cycle of evolution on a galactic scale.
Due to the very different characteristics of its multiple phases, the interstellar medium has to be studied using various observational techniques and different types of telescopes. The coldest components of the interstellar medium do not emit visible light, and require the observation of telescopes sensitive to the weak emission of radio waves that this material produces. Using different radio telescopes, such as the 40-meter diameter of the Yebes Observatory, which the Institute of Radio Astronomy Millimeter, to which the IGN belongs, has in Grenoble and Granada, or the recently opened Atacama Large Millimeter / submillimeter Array in the Atacama desert in Chile, astronomers from the National Astronomical Observatory contribute to characterize the physical and chemical properties of the molecular clouds where stars are born and of the circumestellar shells produced by the stars in the last stages of their lives . The study of these regions is helping to complete our knowledge of the most unknown phases of the complex life cycle of stars.
Answer:
The time period of the motion is, T = 0.03 s
The frequency of the rotation is, f = 30 Hz
Explanation:
Given data,
The rotational speed of an object, ω = 30 rpm
ω = 188.5 rad/s
The time period of motion is,
T = 2π / ω
Substituting the given values in the above equation
= 2π / 188.5
T = 0.03 s
The time period of the motion is, T = 0.03 s
The frequency of rotation,
f = 1 /T
= 1 / 0.03
= 30 Hz
Hence, the frequency of the rotation is, f = 30 Hz
