Answer :
The estimated distance traveled by the race car during the 1-minute period using the velocity at the end of the time intervals is approximately 175.6 miles.
To estimate the distance the race car traveled during the 1-minute period, we can use the velocities at the beginning and end of the time intervals.
a) Using the velocities at the beginning of the time intervals:
The car's initial velocity is given as 182.9 mi/hr at time 0 seconds.
Since the time intervals are 10 seconds apart, we can assume a constant velocity for each interval.
To estimate the distance traveled during each interval, we can multiply the velocity by the time interval (10 seconds) to get the displacement.
The displacement represents the distance traveled during each interval.
Using this method, we can calculate the distance traveled during each interval as follows:
Interval 1: 182.9 mi/hr * 10 s = 1829 mi
Interval 2: 168.0 mi/hr * 10 s = 1680 mi
Interval 3: 106.9 mi/hr * 10 s = 1069 mi
Interval 4: 99.8 mi/hr * 10 s = 998 mi
Interval 5: 124.5 mi/hr * 10 s = 1245 mi
Interval 6: 176.1 mi/hr * 10 s = 1761 mi
Interval 7: 175.6 mi/hr * 10 s = 1756 mi
To find the total distance traveled during the 1-minute period, we sum up the distances traveled during each interval:
Total distance = 1829 + 1680 + 1069 + 998 + 1245 + 1761 + 1756 = 13338 mi
Therefore, the estimated distance traveled by the race car during the 1-minute period using the velocities at the beginning of the time intervals is approximately 13338 miles.
b) Using the velocities at the end of the time intervals:
The car's velocity at the end of the 1-minute period is given as 175.6 mi/hr. We will use this velocity for the entire 1-minute period.
Since the velocity is constant, we can calculate the distance traveled using the formula: distance = velocity * time.
Using this formula, we can calculate the distance traveled during the 1-minute period:
Distance = 175.6 mi/hr * 1 min * (1 hr / 60 min) = 175.6 mi
Therefore, the estimated distance traveled by the race car during the 1-minute period using the velocity at the end of the time intervals is approximately 175.6 miles.
Please note that the estimated distances obtained using the velocities at the beginning and end of the time intervals are different.
The estimate obtained using the velocities at the beginning of the time intervals is 13338 miles, while the estimate obtained using the velocity at the end of the time intervals is 175.6 miles.
The actual distance traveled by the race car during the 1-minute period may lie between these two estimates or may be different altogether.
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