Question

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?

Answer 1

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. 

Answer 2

The correct answer is graph 4.

Step-by-step 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=(\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).