Chapter 4.7, Problem 38E

(a)

To determine

To find: The speed of a car that skids 25 feet.

Answer to Problem 38E

  $s\approx 21.2\text{ miles per hour}$

Explanation of Solution

Given information: Driving: After an accident, police can determine how fast a car was travelling before the driver put on his breaks by using the equation $s=\sqrt{30fd}$ . In this equation, s represents the speed in miles per hour, f represents the coefficient friction and d represents the length of the skid in feet. The coefficient of friction varies with road conditions. Suppose the coefficient of friction is 0.6.

Calculation:

  $s=\sqrt{30fd}$

Replace the variables with given values of f and d

  $f=0.6,d=25$

  $\begin{array}{l}s=\sqrt{30\left(0.6\right)\left(25\right)}\\ s=\sqrt{450}\approx 21.2\end{array}$

  $s\approx 21.2\text{ miles per hour}$

(b)

To determine

How many feet would it take you to stop, if you were driving 35 miles per hour?

Answer to Problem 38E

  $68\text{ feet}$

Explanation of Solution

Given information: Driving: After an accident, police can determine how fast a car was travelling before the driver put on his breaks by using the equation $s=\sqrt{30fd}$ . In this equation, s represents the speed in miles per hour, f represents the coefficient friction and d represents the length of the skid in feet. The coefficient of friction varies with road conditions. Suppose the coefficient of friction is 0.6.

Calculation:

  $s=\sqrt{30fd}$

Replace the variables with given values of s and f

  $f=0.6,s=35$

  $\begin{array}{l}35=\sqrt{30\left(0.6\right)d}\\ 1225=18d\\ \to d\approx 68.06\\ 68\text{ feet}\end{array}$

(c)

To determine

If the speed is doubled, will the skid be twice as long? Explain.

Answer to Problem 38E

No

Explanation of Solution

Given information: Driving: After an accident, police can determine how fast a car was travelling before the driver put on his breaks by using the equation $s=\sqrt{30fd}$ . In this equation, s represents the speed in miles per hour, f represents the coefficient friction and d represents the length of the skid in feet. The coefficient of friction varies with road conditions. Suppose the coefficient of friction is 0.6.

Calculation:

No, this is not a linear function it’s a radical.

Therefore, doubling 1 value doesn’t double the other.