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?

Explanation:

Step1: Recall the direct - variation formula

The formula for direct variation is \(y = kx\), where \(y\) is velocity (\(v\)), \(x\) is time (\(t\)), and \(k\) is the constant of variation (acceleration due to gravity \(g\)). So \(v=gt\).

Step2: Substitute values from the table

Take a pair of values from the table. For example, when \(t = 1\) second and \(v=9.8\) meters per second. Substitute into \(v = gt\): \(9.8=g\times1\).

Answer:

\(9.8\frac{m}{s^{2}}\)