1) a particle moves in a circular path at constant speed. the initial location of the particle is (5.47m,6.09m) at t=3.29 s. the velocity of the particle at this time is 3.07m/s j (i. e., directed along the positive y-axis). acceleration at this time is along the +x axis. at t=9.29 s, v is -3.07m/s i and the acceleration is directed along the +y axis. find the radius of the circle (in meters).
assume that the time interval is less than 1 period.
2) a particle moves in a circular path at constant speed. the initial location of the particle is (4.51m,5.87m) at t=4.2 s. the velocity of the particle at this time is 2.99m/s j (i. e., directed along the positive y-axis). acceleration at this time is along the +x axis. at t=9.27 s, v is -2.99m/s i and the acceleration is directed along the +y axis. find the x-coordinate of the center of the circle (in meters).
assume the time interval is less than 1 period.

1) 3.91 m

2) 7.73 m

Explanation:

For an object moving in a circular path, the velocity is tangential to the circle.  If it's moving at constant speed, the object's acceleration is purely centripetal, so it points towards the center of the circle.

1) Originally, the particle's velocity is in the +y direction, and its acceleration is in the +x direction.  So the particle is at the 9 o'clock position and moving clockwise.

Next, the particle's velocity is in the -x direction, and the acceleration is in the +y direction.  So the particle is at the 6 o'clock position.

Assuming that the time interval is less than 1 period, that means the particle has moved 3/4 of a revolution.

At constant speed, distance = speed × time:

d = v t

3/4 (2π r) = (3.07 m/s) (9.29 s − 3.29 s)

3/2 π r = 18.42 m

r = 3.91 m

2) Using the same logic as the first problem, we know that originally, the particle starts at the 9 o'clock position and moves clockwise to the 6 o'clock position, covering 3/4 of the circle's circumference.

The radius of the circle is:

d = v t

3/4 (2π r) = (2.99 m/s) (9.27 s − 4.2 s)

3/2 π r = 15.16 m

r = 3.22 m

When the particle is originally at the 9 o'clock position, it is directly to the left of the center.  So the x-coordinate of the center is:

x = 4.51 m + 3.22 m

x = 7.73 m

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:

hypothesising or postulating