People hoping to travel to other worlds are faced with huge challenges. one of the biggest is the time required for a journey. the nearest star is 4.1×1016m away. suppose you had a spacecraft that could accelerate at 1.3 g for half a year, then continue at a constant speed. (this is far beyond what can be achieved with any known technology.) part a how long would it take you to reach the nearest star to earth?

The travel would take 6.7 years.

Explanation:

The equation for an object moving in a straight line with acceleration is:

x = x0 + v0 t + 1/2a*t²

where:

x = position at time t

x0 = initial position

v0 = initial velocity

a = acceleration

t = time

In a movement with constant speed, a = 0 and the equation for the position will be:

x = x0 + v t

where v = velocity

Let´s calculate the position from the Earth after half a year moving with an acceleration of 1.3 g = 1.3 * 9.8 m/s² = 12.74  m/s²:

Seconds in half a year:

1/2 year = 1.58 x 10⁷ s

x = 0 m + 0 m/s + 1/2 * 12.74 m/s² * (1.58 x 10⁷ s)²  = 1.59 x 10¹⁵ m

Now let´s see how much time it takes the travel to the nearest star after this half year.

The velocity will be the final velocity achived after the half-year travel with an acceleration of 12.74 m/s²

v = v0 + a t

Since the spacecraft starts from rest, v0 = 0

v = 12.74 m/s² * 1.58 x 10⁷ s = 2.01 x 10 ⁸ m/s

Using the equation for position:

x = x0 + v t

4.1 x 10¹⁶ m = 1.59 x 10¹⁵ m + 2.01 x 10 ⁸ m/s * t

(4.1 x 10¹⁶ m - 1.59 x 10¹⁵ m) / 2.01 x 10 ⁸ m/s = t

t = 2.0 x 10⁸ s * 1 year / 3.2 x 10 ⁷ s = 6.2 years.

The travel to the nearest star would take 6.2 years + 0.5 years = 6.7 years.

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

answer: a) y=-8x+5

a) m= -8

b) m= -2

c) m= 7

d) m= 6