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:
[tex]g=9.81 m/s^2[/tex]
In a speed vs. time graph of an object, the acceleration corresponds to the slope of the curve; in fact, acceleration is defined as
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where [tex]\Delta v[/tex] is the change in velocity and [tex]\Delta t[/tex] 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).
