Example: Chapter 2 Problem 4. At 3 PM a car is located 20 km south of its starting point. One hour later it is 96 km farther south. After two more hours it is 12 km south of the original starting point. (a) What is the displacement of the car between 3 PM and 6 PM?

Example: Chapter 2 Problem 4. At 3 PM a car is located 20 km south of its starting point. One hour later it is 96 km farther south. After two more hours it is 12 km south of the original starting point. (a) What is the displacement of the car between 3 PM and 6 PM?

Answer

Displacement is defined as the change in position of an object (final position - initial position). To solve this, let's establish a coordinate system where North is positive and South is negative, and the original starting point is 0 km. Step 1: Identify the initial position at 3 PM. The problem states the car is 20 km south of the starting point, so x_initial = -20 km. Step 2: Determine the timeframe. The question asks for the displacement between 3 PM and 6 PM. This is a total of 3 hours (1 hour later + 2 more hours). Step 3: Identify the final position at 6 PM. The problem states that after these 3 hours (at 6 PM), the car is 12 km south of the original starting point, so x_final = -12 km. Step 4: Calculate displacement using the formula Delta_x = x_final - x_initial. Delta_x = (-12 km) - (-20 km) = -12 km + 20 km = 8 km. Since the result is positive, the displacement is 8 km North.