Position and Displacement

Describe motion relative to a reference point and calculate signed displacement.

Lesson 1 of 33 parts Practice Flashcards

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Reference Frames and Position

Objective: State a reference point, axis, and coordinate when describing position.

Position x locates an object relative to a chosen origin and positive direction. Position values depend on the reference frame; physical relationships remain consistent when coordinates are transformed properly. A one-dimensional axis requires a sign convention, and the coordinate alone is not a traveled distance. A frame fixed to a moving vehicle can describe different positions and velocities from a ground-fixed frame.

Worked examples

Try itA marker is 4 m west of a post, with east positive. State its position.Show answer

1. Choose the post as x = 0. 2. West is negative under this sign convention. 3. The marker is at x = −4 m.

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Reference Frames and Position

Objective: State a reference point, axis, and coordinate when describing position.

Worked examples

Try itA marker is 4 m west of a post, with east positive. State its position.Show answer

1. Choose the post as x = 0. 2. West is negative under this sign convention. 3. The marker is at x = −4 m.

Distance and Displacement

Objective: Distinguish path length from change in position.

Distance is the nonnegative total length of the path traveled; displacement is the vector change from initial to final position, Δx = x_f − x_i. In one dimension its sign gives direction. A round trip can have positive distance and zero displacement. The magnitude of displacement cannot exceed distance traveled along the path.

Formulas

$Δx = x_f − x_i$

Worked examples

Try itA student walks 5 m east and then 2 m west. Find distance and displacement.Show answer

1. Add path lengths: 5 m + 2 m = 7 m. 2. Choose east positive; the final position is +3 m from the start. 3. Displacement = +3 m, meaning 3 m east.

Signed Directions and Vectors

Objective: Represent directed quantities and interpret sign.

A scalar has magnitude alone, whereas a vector has magnitude and direction. Position change is a vector; path distance is scalar. In one dimension, positive and negative signs encode opposite directions according to the stated axis. Vector components add algebraically, so opposite-direction movements partially cancel when computing displacement. Units remain meters for both distance and displacement.

Worked examples

Try itA cart moves −3 m and then +8 m. Find net displacement.Show answer

1. Write signed changes: −3 m and +8 m. 2. Add: −3 m + 8 m = +5 m. 3. The cart ends 5 m in the positive direction from its start.

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