Question

passage i
students used 2 methods to calculate d, a cars total stopping distance; d is the distance a car travels from the time a driver first reacts to an emergency until the car comes to a complete stop.
in method 1, r is the distance a car travels during a drivers assumed reaction time of 0.75 sec, and b is the average distance traveled once the brakes are applied. method 2 assumes that d = initial speed in ft/sec × 2 sec. table 1 lists r, b, and d for various initial speeds, where d was computed using both methods. figure 1 contains graphs of d versus initial speed for method 1 and method 2.
according to figure 1, the 2 methods yield the same value for d when the initial speed is closest to
a. 20 mi/hr
b. 40 mi/hr
c. 60 mi/hr
d. 80 mi/hr

Explanation:

To find when the two methods yield the same \( D \), we compare \( D \) values from Table 1 for each initial speed:

• At 20 mi/hr: Method 1 \( D = 42 \), Method 2 \( D = 58 \) (difference = 16).
• At 40 mi/hr: Method 1 \( D = 124 \), Method 2 \( D = 118 \) (difference = 6).
• At 60 mi/hr: Method 1 \( D = 246 \), Method 2 \( D = 176 \) (difference = 70).
• At 80 mi/hr: Method 1 \( D = 408 \), Method 2 \( D = 236 \) (difference = 172).

The smallest difference is at 40 mi/hr, so the initial speed closest to where \( D \) values match is 40 mi/hr.

Answer:

B. 40 mi/hr