Which graph represents the relationship between the speed of a freely falling object and the time of fall of the object near Earth’s surface?

After looking closely at the graph you posted above, the one graph that does represent the speed and the time of a freely falling object near the surface of the earth is graph number 4.

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skyluke89 skyluke89 · Answer 2 · 2018-11-03T10:28:51-04:00

The correct answer is graph 4.

Explanation:

An object in free fall near the Earth's surface experiences only one force: the force of gravity, that attracts the object towards the Earth's center. As a result, the acceleration of the object is constant, and it is equal to the gravitational acceleration:

\(g=9.81 m/s^2\)

In a speed vs. time graph of an object, the acceleration corresponds to the slope of the curve; in fact, acceleration is defined as

\(a=\frac{\Delta v}{\Delta t}\)

where \(\Delta v\) is the change in velocity and \(\Delta t\) is the time interval. But in a speed vs. time graph, this ratio corresponds to the slope of the curve, so the slope is equal to the acceleration.

In a motion of free-fall, the acceleration is constant, so the slope must be constant as well: so, only choice (1) or (4) can be right. However, the graph (1) shows an object at constant speed (so, acceleration=0), therefore it cannot be correct: so, the only correct choice is (4).