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?

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:

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

where is the change in velocity and 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).

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