Question
Under ideal conditions, if a person driving a car slams on the brakes and skids to a stop, the length of the skid marks (in feet) is given by the formula$$L(w, v)=k w v^{2}$$where$$\begin{aligned}k &=\text { constant } \\w &=\text { weight of car in pounds } \\v &=\text { speed of car in miles per hour }\end{aligned}$$For $k=0.0000133,$ find $L(2,000,40)$ and $L(3,000,60)$
Step 1
We can do this by plugging these values into the formula: $$ L(2,000, 40) = 0.0000133 \times 2,000 \times 40^2 $$ Now, let's calculate the result: $$ L(2,000, 40) = 0.0000133 \times 2,000 \times 1,600 $$ $$ L(2,000, 40) = 0.0000133 \times Show more…
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Under ideal conditions, if a person driving a car slams on the brakes and skids to a stop, the length of the skid marks (in feet) is given by the formula $$ L(w, v)=k w v^{2} $$ where $$ \begin{aligned} k &=\text { constant } \\ w &=\text { weight of car in pounds } \\ v &=\text { speed of car in miles per hour } \end{aligned} $$ For $k=0.0000133,$ find $L_{w}(2,500,60)$ and $L_{v}(2,500,60)$ and interpret the results.
Multivariable Calculus
Partial Derivatives
Under ideal conditions, if a person driving a car slams on the brakes and skids to a stop, the length of the skid marks (in feet) is given by the formula $$ L=0.0000133 x y^{2} $$ where $x$ is the weight of the car (in pounds) and $y$ is the speed of the car (in miles per hour). What is the average length of the skid marks for cars weighing between 2,000 and 3,000 pounds and traveling at speeds between 50 and 60 miles per hour? Set up a double integral and evaluate it.
Double Integrals over Rectangular Regions
Automobile sidd marks The speed $V$ at which an automobile was traveling before the brakes were applied can sometimes be estimated from the length $L$ of the skid marks. Assume that $V$ is directly proportional to the square root of $L$ (a) Express $V$ as a function of $L$ by means of a formula that involves a constant of proportionality $k$ (b) For a certain automobile on a dry surface, $L=50 \mathrm{ft}$ when $V=35 \mathrm{mi} / \mathrm{hr} .$ Find the value of $k$ in part (a). Estimate the initial speed of the automobile in part (b) if the skid marks are 150 feet long.
Polynomial and Rational Functions
Variation
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