Interpret terms, factors, and coefficients in polynomial and rational expressions.
Determine units and meaning of model components
Problem
Height is \(s(t)~=~-16t^2~+~40t~+~5~\text{feet}\), where \(t\) is in seconds. Interpret each coefficient and constant, including its power, units, and contextual role.
Big Picture
What this problem is really about
Balance units term by term: a coefficient multiplying the input to power k must carry output units divided by input units to that power. Then compare the polynomial with the standard motion form to assign roles. The quadratic coefficient is half the acceleration, the linear coefficient is initial velocity, and the constant is the output at time zero.
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