Question

Suppose the odometer on our car is broken and we want to estimate the distance driven over a 30 second time interval. We take the speedometer readings every five seconds and record them in the following table

Time (s) 0 5 10 15 20 25 30
Velocity (mi/h) 17 21 |24 27 32 31 27
In order to have the time and the velocity in consistent units, let's convert the velocity readings to feet per second 5280 3600 (1 mi/h = ft/s). (Round your answers to the nearest whole number.)
Time (s) 0 10 15 20 25 30
Velocity (ft/s) 25 ___ 35 ____ 47 45 40
During the first five seconds the velocity doesn't change very much, so we can estimate the distance traveled during that time by assuming that the velocity is constant. If we take the velocity during that time interval to be the initial velocity (25 ft/s), then we obtain the approximate distance traveled during the first five seconds:
25 ft/s × 5 s = ______ ft

Answer 1

The distance traveled in the first five seconds is 125 feet, computed by multiplying the constant speed of 25 ft/s by the time interval of 5 seconds.

Step-by-step explanation:

The student's question involves estimating the distance traveled by a car with a broken odometer by using readings from a speedometer. The student has already converted the speed from miles per hour to feet per second, which is a necessary step to have consistent units for speed and time.

To find the distance traveled in the first five seconds where the speed is constant at 25 ft/s, we simply multiply the speed by the time interval. The calculation will be: 25 ft/s × 5 s = 125 ft. Therefore, the distance traveled during the first five seconds is 125 feet.