1D Motion / Kinematics

The x-axis and Reference Points

In one-dimensional motion, we use a single axis—typically the horizontal x-axis—to describe the position of objects. The origin is a chosen reference point on this axis, assigned the value x = 0. All positions are measured relative to this origin.

• Origin: The reference point (x = 0) from which positions are measured.

• x-coordinate: Indicates both the distance from the origin and the direction (positive or negative) along the axis.

• Choice of Origin: The origin can be placed at any convenient location; all other positions are then measured relative to it.

Example: If a car is 2.5 km west of a turnoff (origin), its position is x = -2.5 km. If the car is chosen as the origin, the turnoff is at x = +2.5 km, and a sign 1 km further west is at x = -1 km.

Summary of 1D Motion

• One-dimensional motion occurs along a straight line and requires only one axis (x-axis) for measurement.

• The origin is the reference point (x = 0).

• The position of an object is described by its x-coordinate, indicating both distance and direction from the origin.

• For two-dimensional motion, both x- and y-axes are needed.

Distance and Displacement

When describing how far an object moves, we distinguish between distance and displacement:

• Distance: The total length of the path traveled, regardless of direction. It is always positive and is a scalar quantity (has magnitude only). The SI unit is the metre (m).

• Displacement: The straight-line change in position from the initial to the final point. It has both magnitude and direction, making it a vector quantity. The SI unit is also the metre (m).

• In 1D motion, displacement can be positive (movement in the positive x-direction) or negative (movement in the negative x-direction).

Formula for Displacement:

Scalar and Vector Quantities

• Scalar Quantity: Described by a single number (with unit), such as mass (6 kg) or temperature (-3 °C). Scalars can be positive, negative, or zero.

• Vector Quantity: Has both magnitude and direction. The magnitude is always positive or zero, but the direction can be specified (e.g., east, west, positive x, negative x).

Worked Example: Bird's Journey

Problem: A bird flies 3 km east, then 3 km north.

• a) Distance traveled: The total path length is 3 km + 3 km = 6 km.

• b) Displacement: The straight-line distance from the starting point to the final position forms the hypotenuse of a right triangle.

Calculation:

The direction is northeast, at a 45° angle from the east axis.

Displacement vs. Distance: Path Dependence

• Distance depends on the actual path taken and accumulates all movement, regardless of direction.

• Displacement depends only on the initial and final positions, not on the path taken.

Example: A board rider follows a curved river path. The distance is the length of the river traveled, while the displacement is the straight-line distance from the starting point to the endpoint.

Summary Table: Scalars vs. Vectors

Additional info: Table entries for mass and velocity are inferred for completeness.