you are driving at a constant speed of 50 mi/h along a straight road at a constant speed between A and B along the way you pass through city C. the cities B and C are 100 and 25 miles resorctively from city A
Use absolute value function to express this distance as a function of T
To express the distance as a function of time (T), we need to consider three scenarios:
Scenario 1: When T < 0
In this case, the car has not yet started its journey from city A. Therefore, the distance covered would be 0 miles. We can express this as:
d(T) = 0
Scenario 2: When 0 ≤ T ≤ 100/50 = 2
In this scenario, the car is traveling from city A towards city B. Since the car is driving at a constant speed of 50 mi/h, the distance covered would be the product of the speed and time. We can express this as:
d(T) = 50 * T
Scenario 3: When 2 < T ≤ 125/50 = 2.5
In this scenario, the car has already reached city B and continues to drive towards city C. The distance covered in this case would be the sum of the distance from A to B (100 miles) and the product of the speed and the time difference between T and 2. We can express this as:
d(T) = 100 + (50 * (T - 2))
Putting it all together, we can define the absolute value function to express the distance as a function of T:
d(T) = |d(T)|
= |0|, if T < 0
= |50 * T|, if 0 ≤ T ≤ 2
= |100 + (50 * (T - 2))|, if 2 < T ≤ 2.5
Note: The absolute value function ensures that the distance is always positive, regardless of the value of T.