Motion in a Straight Line - Vocabulary Flashcards

Vocabulary flashcards covering key terms and concepts from the Motion in a Straight Line lecture notes.

Distance

Total length of the path traveled; a scalar quantity that depends only on magnitude, not direction.

Displacement

The shortest straight-line vector from the initial to the final position; magnitude is the straight-line distance and has a direction.

Speed

Rate at which distance is covered; a scalar quantity representing how fast an object moves.

Velocity

Rate of change of position with time; a vector quantity that includes both speed and direction.

Average Speed

Total distance traveled divided by total time taken.

Average Velocity

Total displacement divided by total time taken; a vector quantity.

Displacement Vector

The vector Δr = rfinal − rinitial; points from the start to the end position.

Position Vector

The vector r = x i + y j + z k representing a point’s location in space relative to the origin.

i, j, k (Unit Vectors)

Unit vectors along the x, y, and z axes used to express vectors in component form.

Magnitude of a Vector

Length of the vector; for components (vx, vy, vz), |v| = \sqrt{vx^2 + vy^2 + v_z^2} .

3D Distance Formula

Distance between two points (x1,y1,z1) and (x2,y2,z2): \sqrt{(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2} .

Cube Space Diagonal

Body diagonal of a cube with side a; length is \sqrt{3} a .

Cube Face Diagonal

Diagonal on a cube’s face; length is \sqrt{2} a .

Room Displacement Example (3-4-5)

For a room with dimensions 3, 4, 5 (units), displacement from one corner to the opposite corner is \sqrt{3^2+4^2+5^2} = 5\sqrt{2} units.

Shortest Path

The straight-line path between two points; its length equals the magnitude of the displacement.

Displacement Components

Displacement expressed along axes: \Delta r = \Delta x \mathbf{i} + \Delta y \mathbf{j} + \Delta z \mathbf{k} .

Displacement Magnitude Formula Example

If \Delta x = \Delta y = \Delta z = a , then \Vert \Delta r \Vert = \sqrt{a^2 + a^2 + a^2} = \sqrt{3} a .

Equal-Time Average Speed Rule

If motion is divided into equal time intervals with speeds \text{V1, V2, …} , then \text{V}_{avg} = \frac{(\text{V1 + V2 + …})}{n} .

Equal-Distance Average Speed Rule

If motion is divided into equal distances \text{d1, d2, …} , then \text{V}_{avg} = \frac{(\text{d1 + d2 + …})}{(\text{d1/v1 + d2/v2 + …})} .

Path vs Displacement Distinction

Path length (distance) is the total length traveled; displacement is the straight-line vector from start to end.

Vector Addition in Components

When adding displacements, add corresponding components: if \mathbf{r1} = \text{(x1, y1, z1)} and \mathbf{r2} = \text{(x2, y2, z2)} , then \mathbf{r1} + \mathbf{r2} = \text{(x1+x2, y1+y2, z1+z2)} .