Question

the velocity, v, of a falling object varies directly to the time, t, of the fall. if after 2 seconds, the velocity of the object is 64 feet per second, what is the velocity after 7 seconds? feet per second question help: video message instructor submit question

Explanation:

Step1: Find the constant of variation

Since \(v\) varies directly with \(t\), the equation is \(v = kt\). When \(t = 2\) and \(v=64\), substitute into the equation: \(64=k\times2\). Solve for \(k\): \(k=\frac{64}{2}=32\).

Step2: Calculate the velocity at \(t = 7\)

Now that \(k = 32\), use the equation \(v=kt\) with \(t = 7\). So \(v=32\times7 = 224\).

Answer:

224