Question

this relationship is given by the equation, ( v = gt ). in this equation, ( g ) is the acceleration due to gravity, ( t ) is the number of seconds, and ( v ) is the velocity of the falling object. note that ( g ) is a constant. find and interpret the meaning of the initial value and the rate of change in this context. the initial value is 0. that means that objects initial velocity 0 m/s. the rate of change is 98. that means the acceleration due to gravity is ( 98.0 m/s^{2} ). the initial value is 0. that means that objects initial velocity 0 m/s. the rate of change is 9.8. that means the acceleration due to gravity is ( 9.8 m/s^{2} ). the initial value is 9.8. that means that objects initial velocity 9.8 m/s. the rate of change is 9.8. that means the acceleration due to gravity is ( 9.8 m/s^{2} ). the initial value is 9.8. that means that objects initial velocity 9.8 m/s. the rate of change is 0.98. that means the acceleration due to gravity is ( 0.98 m/s^{2} ).

Explanation:

Step1: Analyze the initial value

The equation is \(v = gt\). When \(t = 0\) (initial time), \(v=0\). So the initial value (when \(t = 0\)) of the velocity \(v\) is \(0\) m/s.

Step2: Analyze the rate of change

The equation \(v = gt\) is in the form \(y = mx\) (where \(y = v\), \(x=t\), \(m = g\)). The rate of change (slope) is \(g\). The standard value of acceleration due to gravity \(g = 9.8\) m/s².

Answer:

The initial value is 0. That means that object's initial velocity 0 m/s. The rate of change is 9.8. That means the acceleration due to gravity is 9.8 m/s². (Second option)