Question

At 3 P.M. a car is located \(20 \mathrm{km}\) south of its starting point. One hour later it is \(96 \mathrm{km}\) farther south. After two more hours, it is \(12 \mathrm{km}\) south of the original starting point. (a) What is the displacement of the car between 3 P.M. and 6 P.M.? (b) What is the displacement of the car from the starting point to the location at 4 P.M.? (c) What is the displacement of the car between 4 P.M. and 6 P.M.?

Short answer

Answer: The car's displacements are -8 km (8 km north) between 3 P.M. and 6 P.M., 116 km south from the starting point to the position at 4 P.M., and -104 km (104 km north) between 4 P.M. and 6 P.M.

Step-by-step solution

Calculate the car's position at 4 P.M.

At 3 P.M., the car is 20 km south of its starting point. By 4 P.M., the car has gone 96 km further south. To find the total distance south from the starting point at 4 P.M., add the initial 20 km and the additional 96 km together. Total distance south at 4 P.M. = 20 km + 96 km = 116 km

Calculate the car's displacement between 3 P.M. and 6 P.M.

To find the displacement between 3 P.M. and 6 P.M., we need to use the car's position at 3 P.M. (20 km south) and its position at 6 P.M. (12 km south). The displacement is defined as the change in position, so we subtract the initial position from the final position: Displacement (3 P.M. to 6 P.M.) = Final Position - Initial Position Displacement (3 P.M. to 6 P.M.) = 12 km - 20 km = -8 km Since the result is negative, it means the car has moved 8 km in the opposite direction, i.e., 8 km northwards.

Calculate the car's displacement from the starting point to the location at 4 P.M.

The displacement from the starting point to the position at 4 P.M. is calculated using the total distance south at 4 P.M which we found in step 1 (116 km). Since the car has moved south from the starting point, the displacement will be positive and equal to the total distance south: Displacement (Starting Point to 4 P.M.) = 116 km

Calculate the car's displacement between 4 P.M. and 6 P.M.

To find the displacement between 4 P.M. and 6 P.M., we will use the car's position at 4 P.M. (116 km south) and its position at 6 P.M. (12 km south). As before, we subtract the initial position from the final position: Displacement (4 P.M. to 6 P.M.) = Final Position - Initial Position Displacement (4 P.M. to 6 P.M.) = 12 km - 116 km = -104 km Since the result is negative, it means the car has moved 104 km in the opposite direction, i.e., 104 km northwards. In summary: a) The car's displacement between 3 P.M. and 6 P.M. is -8 km (8 km north). b) The car's displacement from the starting point to the position at 4 P.M. is 116 km south. c) The car's displacement between 4 P.M. and 6 P.M. is -104 km (104 km north).