Answer:
d d d d dd d d d d d dd d d d d dd d
Objects with equal speeds definitely have equal velocities. -- FALSE. For equal velocities, they also have to be going in the same direction.
If you are given an object's velocity, you can definitely determine its speed. -- TRUE. If you know the velocity, then you know both the object's speed and its direction.
If you know the distance an object travels, and the time it takes to do so, you can determine the object's velocity. -- FALSE. Knowing the distance and time, you can figure out the object's speed. But if you don't also know the direction it's moving, then you can't say what its velocity is.
If an object moves at constant speed, it must also be moving at constant velocity. -- FALSE. Besides constant speed, it also needs to move in a straight line to have constant velocity. If it turns, its velocity changes, even if its speed doesn't.
If an object moves at constant velocity, it must also be moving at constant speed. -- TRUE. Constant velocity means its speed AND its direction are not changing.
Objects with equal velocities definitely have equal speeds. -- TRUE. If their velocities are equal, then their speeds are equal AND they're moving in the same direction.
After laboring through this one, I'm wondering if there can possibly be any more ways to say the same thing.
I believe it is call “Acceleration”
You asked a question. I'm about to answer it.
Sadly, I can almost guarantee that you won't understand the solution.
This realization grieves me, but there is little I can do to change it.
My explanation will be the best of which I'm capable.
Here are the Physics facts I'll use in the solution:
-- "Apparent magnitude" means how bright the star appears to us.
-- "Absolute magnitude" means the how bright the star WOULD appear
if it were located 32.6 light years from us (10 parsecs).
-- A change of 5 magnitudes means a 100 times change in brightness,
so each magnitude means brightness is multiplied or divided by ⁵√100 .
That's about 2.512... .
-- Increasing magnitude means dimmer.
Decreasing magnitude means brighter.
+5 is 10 magnitudes dimmer than -5 .
-- Apparent brightness is inversely proportional to the square
of the distance from the source (just like gravity, sound, and
the force between charges).
That's all the Physics. The rest of the solution is just arithmetic.
____________________________________________________
-- The star in the question would appear M(-5) at a distance of
32.6 light years.
-- It actually appears as a M(+5). That's 10 magnitudes dimmer than M(-5),
because of being farther away than 32.6 light years.
-- 10 magnitudes dimmer is ( ⁵√100)⁻¹⁰ = (100)^(-2) .
-- But brightness varies as the inverse square of distance,
so that exponent is (negative double) the ratio of the distances,
and the actual distance to the star is
(32.6) · (100)^(1) light years
= (32.6) · (100) light years
= approx. 3,260 light years . (roughly 1,000 parsecs)
I'll have to confess that I haven't done one of these calculations
in over 50 years, and I'm not really that confident in my result.
If somebody's health or safety depended on it, or the success of
a space mission, then I'd be strongly recommending that you get
a second opinion.
But, quite frankly, I do feel that mine is worth the 5 points.
