Question

6 explain the difference between distance and displacement. 7 what is the displacement of a locomotive that changes its position from 25mw to 76mw? 8 a car changes its position from 52kmw to 130kme. what is the cars displacement? 9 determine the total displacement for each of the following motions by algebraic methods.

Explanation:

Step1: Determine the formula for displacement

Displacement is the difference between the final and initial positions. If we take the west - east direction into account, we can assign a sign convention. Let's assume the east direction is positive and the west direction is negative.

Step2: Calculate the displacement for the locomotive

The initial position of the locomotive \(x_{i}=- 25m\) (west is negative) and the final position \(x_{f}=-76m\).
The displacement formula is \(\Delta x=x_{f}-x_{i}\)
Substitute the values: \(\Delta x=-76 - (-25)\)

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The negative sign indicates the direction is west.

Step3: Calculate the displacement for the car

The initial position of the car \(x_{i}=-52km\) (west is negative) and the final position \(x_{f}=130km\) (east is positive)
Using the displacement formula \(\Delta x=x_{f}-x_{i}\)
Substitute the values: \(\Delta x = 130-(-52)\)

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$$

The positive sign indicates the direction is east.

Answer:

• For the locomotive: The displacement is \(51m\) west.
• For the car: The displacement is \(182km\) east.