Question

if an object is shot upward with an initial velocity, ( v_0 ), in feet per second (ft/s), the velocity, ( v ), in ft/s is given by the formula ( v = v_0 - 32t ), where ( t ) is time in seconds. find the initial velocity of an object if the velocity after 2 seconds is 42 ft/s.

Explanation:

Step1: Substitute the values into the formula

Given \(v = 42\) ft/s, \(t = 2\) s. Substitute into \(v=v_{0}-32t\), we get \(42 = v_{0}-32\times2\).

Step2: Solve for \(v_{0}\)

First, calculate \(32\times2 = 64\). Then the equation becomes \(42=v_{0}-64\). Add 64 to both sides: \(v_{0}=42 + 64\).

Answer:

\(106\) ft/s