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. the acceleration due to gravity is the constant of variation. what is the acceleration due to gravity of a falling object? velocity of a falling object time (seconds) velocity (meters/second) 0 0 1 9.8 2 19.6 3 29.4 4 39.2 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 the direct - variation formula

The formula for direct variation is \(y = kx\), where \(y\) is the dependent variable, \(x\) is the independent variable, and \(k\) is the constant of variation. In this case, velocity \(v\) varies directly with time \(t\), so \(v=kt\).

Step2: Find the constant of variation \(k\)

We can use any pair of values from the table. Let's take \(t = 1\) second and \(v=9.8\) meters/second. Substitute into \(v = kt\):
\(9.8=k\times1\)

Answer:

\(9.8\frac{m}{s^{2}}\) (the second option)