Chuck Wagon travel with a constant velocity of 0.98 miles/minute for 9.3 minutes. Chuck then decelerates at -0.11 miles/min/min for 1.8 minutes. Determine the total distance traveled by Chuck Wagon (in miles).
recall that s = vt + 1/2 at^2
The total distance is thus
.98*9.3 + .98*1.8 - 0.11/2 * 1.8^2
To determine the total distance traveled by Chuck Wagon, we need to calculate the distance traveled during both the constant velocity and deceleration periods.
1. Distance during constant velocity:
Given that Chuck Wagon traveled with a constant velocity of 0.98 miles/minute for 9.3 minutes, we use the formula:
Distance = Velocity × Time
Distance during constant velocity = 0.98 miles/minute × 9.3 minutes = 9.114 miles
2. Distance during deceleration:
During the deceleration period, the velocity is changing at a rate of -0.11 miles/minute/minute for 1.8 minutes. To find the distance during deceleration, we can use the following formula:
Distance = Initial Velocity × Time + (Acceleration × Time^2) / 2
Since the initial velocity is given as 0.98 miles/minute and the acceleration is -0.11 miles/minute/minute, and the time is 1.8 minutes, we can substitute those values into the formula:
Distance during deceleration = 0.98 miles/minute × 1.8 minutes + (-0.11 miles/minute/minute × (1.8 minutes)^2) / 2
Distance during deceleration = 1.764 - 0.1782 = 1.5858 miles
3. Total distance traveled by Chuck Wagon:
To find the total distance, we add the distances during constant velocity and deceleration:
Total distance = Distance during constant velocity + Distance during deceleration
Total distance = 9.114 miles + 1.5858 miles = 10.6998 miles
Therefore, the total distance traveled by Chuck Wagon is approximately 10.70 miles.