Let a particle move from Xo to X following the curved path.

Question

ScanSolve AI Tutor · Accepted Answer

Here's an explanation of the example shown on the slide:

Identify initial and final positions.
From the graph and the given displacement calculation, the particle starts at an initial position $X_0 = 0 \text{ m}$ and moves to a final position $X = 25 \text{ m}$ .
Calculate the displacement.
Displacement is the straight-line distance from the initial to the final position, including direction.
$\text{Displacement} = X - X_0$ $\text{Displacement} = 25 \text{ m} - 0 \text{ m} = 25 \text{ m}$
Since the final position is to the right of the initial position, the displacement is to the right.
The displacement is $\boxed{\text{25 m to the right}}$ .
Calculate the distance.
Distance is the total length of the path traveled. The particle moves from $0 \text{ m}$ to a maximum point (which appears to be $35 \text{ m}$ on the graph) and then turns back to $25 \text{ m}$ .
The distance traveled to the right is $35 \text{ m} - 0 \text{ m} = 35 \text{ m}$ .
The distance traveled to the left (backwards) is $35 \text{ m} - 25 \text{ m} = 10 \text{ m}$ .
$\text{Distance} = (\text{path to max point}) + (\text{path back to final point})$ $\text{Distance} = 35 \text{ m} + 10 \text{ m} = 45 \text{ m}$
The total distance traveled is $\boxed{\text{45 m}}$ .

Answer