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What does a downward sloping diagonal line mean in a velocity vs time graph?
This means your velocity is decreasing with time, or in other words, the object is slowing down.
What is the skydiver's downward velocity at that instant just before starting to fall?
The same as that of the aircraft that he /she is in. If flying level, it would be zero.
Is the total time of a ball thrown upwards is it equal to the total time of the downward velocity?
There's no such thing as "time of the downward velocity", but I think I get the sense of your question. If the effects of air resistance can be disregarded, then any object thrown upwards spends half of its time rising, and the identical amount of time falling back to the height of your hand when you let it go.
If a small marble is dropped straight downward what is the initial velocity of the marble?
The initial velocity is zero. In most basic physics problems like this one the initial velocity will be zero as a rule of thumb: the initial velocity is always zero, unless otherwise stated, or this is what you are solving for Cases where the initial velocity is not zero examples a cannon ball is shot out of a cannon at 50 mph a ball is thrown from at a speed of 15 mph etc
A squirrel drops a nut over a cliff what is the velocity of the nut after 3 seconds?
Ignoring air resistance, the velocity of any object that goes off a cliff is 29.4 meters (96.5 feet) per second downward, after 3 seconds in free-fall.
