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 direct variation formula

The formula for direct variation is \(y = kx\), where \(k\) is the constant of variation. Here, velocity \(v\) varies directly with time \(t\), so \(v=kt\).

Step2: Substitute values from the table

Take \(t = 1\) and \(v=9.8\). Substitute into \(v = kt\): \(9.8=k\times1\).

Answer:

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