Question

the velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table. velocity of a falling object

time (seconds)	velocity (meters/second)
1	9.8
2	19.6
3	29.4
4	39.2

the acceleration due to gravity is the constant of variation. what is the acceleration due to gravity of a falling object?
4.9 \\(\frac{m}{s^{2}}\\)
9.8 \\(\frac{m}{s^{2}}\\)
10.2 \\(\frac{m}{s^{2}}\\)
19.6 \\(\frac{m}{s^{2}}\\)

Explanation:

Step1: Recall acceleration - velocity relation

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Step2: Select two - point data

Let's take the first two points $(t_1 = 0,v_1 = 0)$ and $(t_2=1,v_2 = 9.8)$.

Step3: Calculate acceleration

$a=\frac{v_2 - v_1}{t_2 - t_1}=\frac{9.8 - 0}{1 - 0}=9.8\frac{m}{s^2}$.
We can also check with other pairs. For example, taking $(t_1 = 1,v_1 = 9.8)$ and $(t_2 = 2,v_2=19.6)$, $a=\frac{19.6 - 9.8}{2 - 1}=9.8\frac{m}{s^2}$.

Answer:

$9.8\frac{m}{s^2}$