Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Based on data from the U.S. Bureau of Public Roads, a model for the total stopping distance of a moving car in terms of its speed is s = 1.1v+ 0.054v2, where s is measured in ft and v in mph. The linear term 1.1y models the distance the car travels during the time the driver per-ceives a need to stop until the brakes are applied, and the quadratic term 0.054y2 models the additional braking distance once they are applied. Find ds/dv at v = 35 and v = 70 mph, and interpret the meaning of the derivative.
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