Answer:
- object is moving to the right with constant speed
- object is moving to the left with constant speed
- object was stationary for a while, then started moving to the right with constant speed
Step-by-step explanation:
These graphs are of position, so the slope of the graph is the change of position with time, which is velocity. When the slope is positive, the velocity is positive, meaning its direction is to the right. When the slope is negative, the velocity is negative, meaning its direction is to the left.
When the slope is zero, the object is stationary (not moving). The position remains as it was.
1. The position vs. time curve is a straight line with positive slope. The object is moving to the right with constant velocity.
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2. The position vs. time curve is a straight line with negative slope. The object is moving to the left with constant velocity.
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3. The position vs. time curve is flat for a while, then increasing with constant slope. The object stayed where it was for a while, then began moving to the right (to larger values of x) with constant velocity.
First I'm going to go through the choices with you and evaluate
each one. Then after that, I'm going to hand you a secret that
I promise is going to knock your socks off.
a- Calculate the ratio of the diameter to the radius for each circle
and show that they are equal.
-- That won't tell you anything. The ratio of the diameter
to the radius of EVERY circle is 2 .
b- Calculate the ratio of degrees to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The circumference
of EVERY circle subtends a central angle of 360°.
c- Calculate the ratio of the área to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the area
to the circumference of EVERY circle is (radius/2).
They're only equal if the circles are the same size.
d- Calculate the ratio of the diameter to the circumference for each circle
and show that they are equal.
-- That doesn't tell you anything. The ratio of the diameter
to the circumference of EVERY circle is 1/pi. If the ratio isn't
1/pi, then you're not looking at a circle.
None of these choices tells you whether the two circles are similar.
What are you going to do ? How can you tell ? ?
Here's the surprise I promised you.
Beware of flying socks:
All circles are similar to all other circles.
Good night.
