Question

(6) what is the distance and displacement of a sprinter when he completes the 100m dash?
distance = _______________
displacement = _______________

(7) your physics teacher walks once around the classroom as shown in the diagram below. what distance does he walk and what is his displacement?
diagram: a rectangle with vertical sides labeled 10.5 m, horizontal sides labeled 8.0 m, with start/end at the bottom right corner

Explanation:

Question (6)

Step1: Define Distance and Displacement

Distance is the total length of the path covered. Displacement is the straight - line distance between the initial and final positions, along with direction.

Step2: Analyze the 100m Dash

In a 100m dash, the sprinter starts at the starting line and runs to the finish line which is 100m away in a straight - line path (assuming a standard straight - track 100m race). So the total path length (distance) is \( 100 \, \text{m} \). The initial position is the starting line and the final position is the finish line, which are 100m apart. So displacement is also \( 100 \, \text{m} \) (in the direction from start to finish). Wait, but maybe the question is considering that after running, he is at the same position? No, that's not the case for a 100m dash. Maybe there is a mis - understanding. Alternatively, if we consider that the sprinter runs 100m and then comes back, but that's not a 100m dash. A 100m dash is a sprint from start to finish (100m). So:

Distance: The sprinter runs 100m, so distance = \( 100 \, \text{m} \)
Displacement: The change in position from start to finish is 100m (since start and finish are 100m apart in a straight line), so displacement = \( 100 \, \text{m} \) (in the direction of running). But maybe the question has a different intention. If we assume that the dash is a circular track or something, but 100m dash is straight. Alternatively, maybe the question is wrong, but based on standard 100m dash:

Wait, no, I think I made a mistake. In a 100m dash, the sprinter starts at a point, runs 100m to the finish line. So distance is 100m, displacement is 100m (from start to finish). But maybe the question is considering that after the race, the sprinter is at rest at the finish line, so displacement is 100m.

Question (7)

Step1: Calculate Distance

The teacher walks around a rectangle. The formula for the perimeter of a rectangle is \( P = 2\times(l + w) \), where \( l \) is the length and \( w \) is the width. Here, \( l = 10.5 \, \text{m} \) and \( w = 8.0 \, \text{m} \).
So, \( P=2\times(10.5 + 8.0)=2\times18.5 = 37 \, \text{m} \). Distance is the total path length, so distance = \( 37 \, \text{m} \).

Step2: Calculate Displacement

Displacement is the straight - line distance between the initial and final positions. Since the teacher starts and ends at the same point (Start/End), the displacement is \( 0 \, \text{m} \).

Answer:

Distance = \( 100 \, \text{m} \)
Displacement = \( 0 \, \text{m} \) (assuming the dash is a straight - line race from start to finish and back to start? No, wait, 100m dash is from start line to finish line which is 100m away. Wait, correction: In a 100m dash, the sprinter runs from the starting point to the finish point which is 100m away in a straight line (usually). Wait, no, actually, in a standard 100m dash, the sprinter starts at one point and runs to a point 100m away along a straight track. So distance is the total path length, which is 100m. Displacement is the straight - line distance from start to end. If it's a straight - line 100m dash (from start to finish, not a round - trip), then displacement is also 100m? Wait, no, maybe I made a mistake. Wait, the 100m dash is a straight - line race where the sprinter starts at the starting line and finishes at the finish line which is 100m away in the same direction. So distance (total path) is 100m, displacement (change in position) is also 100m? But maybe the question assumes that after completing the dash, he comes back? No, the 100m dash is a one - way race. Wait, maybe the original thought was wrong. Let's re - think: Distance is the total length of the path traveled. In a 100m dash, the sprinter runs 100m from start to finish, so distance is 100m. Displacement is the vector from initial position to final position. If the start and finish are 100m apart in a straight line, displacement is 100m. But maybe the question has a different context. Wait, maybe it's a round - trip? No, 100m dash is not a round - trip. Alternatively, maybe the question is considering that after running 100m, he is at the finish line, so displacement is 100m. But I think I made a mistake earlier. Let's correct: