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 0 1 2 3 4 0 9.8 19.6 29.4 39.2 4.9 9.8 10.2 19.6

Explanation:

Step1: Recall the formula for direct variation

If \(y\) varies directly with \(x\), then \(y = kx\), where \(k\) is the constant of variation. Here, velocity \(v\) varies directly with time \(t\), so \(v=kt\).

Step2: Substitute values from the table to find \(k\)

Take the first non - zero pair from the table: when \(t = 1\) second and \(v=9.8\) m/s. Substitute into \(v = kt\).
We get \(9.8=k\times1\).

Answer:

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