Consider the question: "An object is traveling at a velocity of 9 ft/s and an acceleration of 2 ft/s2. Estimate the change in position in the next 4 seconds."
1. In physics, one of the kinematic formulas is ∆x = v0∆t + 1/2 a(∆t)^2 where ∆x is change in position, v0 is initial velocity, a is acceleration, and ∆t is the change in time. Use this
formula to answer the question above (no complete sentences needed).Then In calculus, the Taylor Polynomial of order 2 is
T2(x) = f(a)+f′(a)(x−a)+ 1/2 f′′(a)(x−a)^2. In complete sentences, how is this function related to the kinematic formula above? Ensure you define all variables (what does f
represent, f′(a) represent,...). In the context to the original question, what would the
f(a) represent?