Question

use this graph below for this question. position of a runner moving in a straight line what is the total distance and displacement for the runner shown in the graph? a distance = 250 m, displacement = 35 m...

Explanation:

Step1: Analyze Distance (Sum of Paths)

The runner moves from 0 to 145 m (first segment), stays (distance 0), then moves back from 145 m to 0, then to 15 m? Wait, no, let's re - examine. Wait, the graph: first, the runner goes from position 0 to 145 m (let's assume the peak is 145 m). Then, from 145 m back to 0 (distance 145 m), then from 0 to 15 m? Wait, no, maybe the graph's axes: y - axis is position (meters), x - axis is time (seconds). Let's assume the first part: from t = 0, position 0 to t = 70 (approx), position 145 m (distance 145 m). Then, from t = 70 to t = 80 (approx), position constant (distance 0). Then, from t = 80 to t = 110 (approx), position goes from 145 m to 0 (distance 145 m). Then, from t = 110 to t = 120 (approx), position goes from 0 to 15 m (distance 15 m)? Wait, no, maybe the correct way: distance is the total length of the path. Let's assume the first segment: 145 m (from 0 to 145), second segment: 145 m (from 145 back to 0), third segment: 15 m (from 0 to 15)? No, maybe the graph is: starts at 0, goes up to 145 m (distance 145), then down to 0 (distance 145), then up to 15 m? Wait, no, the final position is 15 m? Wait, the problem's options: let's see the options (even though some are blurry). Wait, distance is sum of all movements: if first movement is 145 m (from 0 to 145), second is 145 m (from 145 to 0), third is 15 m (from 0 to 15)? No, maybe the correct calculation: distance = 145 + 145+15? No, wait, maybe the peak is 145 m, then back to 0 (145 m), then to 15 m (15 m). So total distance = 145 + 145+15 = 305? No, maybe the graph is: first, from 0 to 145 (145 m), then from 145 to 0 (145 m), then from 0 to 15 (15 m). Wait, but displacement is final position - initial position. Initial position is 0, final position is 15 m? No, maybe I misread. Wait, the correct approach:

Distance: sum of magnitudes of each displacement.

1. First part: from 0 to 145 m: distance = 145 m.

1. Second part: from 145 m to 0 m: distance = 145 m.

1. Third part: from 0 m to 15 m: distance = 15 m.

Total distance = 145 + 145+15 = 305? No, maybe the third part is not there. Wait, maybe the graph is: starts at 0, goes to 145, then back to 0, then to 15? Or maybe the final position is 15 m. Displacement is final position - initial position = 15 - 0 = 15 m.

Wait, let's check the options. One option is Distance = 305 m, Displacement = 15 m. Let's verify:

First movement: 145 m (0 to 145).

Second movement: 145 m (145 to 0).

Third movement: 15 m (0 to 15).

Total distance: 145 + 145+15 = 305 m.

Displacement: 15 - 0 = 15 m.

Step2: Analyze Displacement (Final - Initial)

Initial position \( x_i = 0 \) m.

Final position \( x_f = 15 \) m (assuming the last part goes to 15 m).

Displacement \( \Delta x=x_f - x_i=15 - 0 = 15 \) m.

Distance is the sum of all path lengths: 145 (first) + 145 (second) + 15 (third) = 305 m.

Answer:

Distance = 305 m, Displacement = 15 m (assuming the correct option with these values, likely the one with Distance = 305 m and Displacement = 15 m)