Choose the graph that best describes the following:
The velocity of a heavy stone (Y) after being dropped from a great height as a function of time (X).
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Choose the graph that best describes the following:
The velocity of a heavy stone (Y) after being dropped from a great height as a function of time (X).
Since the velocity depends on the acceleration in a direct relationship, and since the acceleration is constant, the graph must have a straight slope.
Since the graph in answer D describes a constant function, this is the correct answer.
In what domain does the function increase?
In free fall, gravity provides constant acceleration (about 9.8 m/s²). Since velocity = acceleration × time, and acceleration is constant, the graph must be a straight line starting from zero.
The slope represents the acceleration due to gravity. A steeper slope means greater acceleration, while the slope stays constant throughout the fall.
At time zero, the stone is just dropped (not thrown), so its initial velocity is zero. The line must pass through (0,0) since v = 0 when t = 0.
Yes! With air resistance, the acceleration decreases as velocity increases, making the graph curved rather than linear. But this problem assumes no air resistance.
A position graph for free fall would be parabolic (curved) because position = ½gt². A velocity graph is linear because velocity = gt.
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