Question

1. for these problems, draw a sketch then solve for distance and for displacement.

a. dj likes to ride his bike around the block. if he rides out of his house to the west, the sidewalk circles the block, and brings him back to his doorstep 0.35 miles later. find his distance and displacement.

b. nicole parks her car at target and walks 150 feet north to get to the store. on her way back to her car she walks 50 ft before pausing when she sees a sign for discounted iced coffee at starbucks. find her distance and displacement.

Explanation:

Part a

Step1: Define Distance and Displacement

• Distance is the total length of the path traveled. Displacement is the straight - line distance from the initial position to the final position, with direction.
• DJ starts at his house, rides around the block, and comes back to his house.

Step2: Calculate Distance

• The total path he traveled is 0.35 miles. So, distance $d = 0.35$ miles.

Step3: Calculate Displacement

• Since his initial position (house) and final position (house) are the same, the displacement $s=0$ miles (because the straight - line distance between the same point is zero).

Step1: Define Distance and Displacement

• Distance is the sum of all the lengths of the paths traveled. Displacement is the straight - line distance from the initial position (car) to the final position (where she paused), with direction.

Step2: Calculate Distance

• Nicole walks 150 feet north to the store and then 50 feet back towards the car. So, total distance $d=150 + 50=200$ feet.

Step3: Calculate Displacement

• Her initial position is at the car (let's consider this as the origin). She moves 150 feet north and then 50 feet south. The displacement $s = 150-50 = 100$ feet north (or we can say the displacement is 100 feet from the car towards the north direction of the store).

Answer:

Distance: 0.35 miles, Displacement: 0 miles

Part b