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Scalar Quantity

A measurement that has magnitude (size) only and no direction (e.g., 5 km, time, speed, distance).

Vector Quantity

A measurement that includes both magnitude (size) and direction (e.g., 5 km [N], displacement, velocity, force).

Position

Position is a vector quantity that specifies an object's location relative to a reference point in space, usually expressed in coordinates.

Distance (d)

A scalar quantity that measures the total path length traveled by an object, regardless of direction.

Displacement (Δd)

A vector quantity that represents the change in position of an object, defined as the shortest distance from the initial to the final position, along with its direction.

Speed (s)

Speed is a scalar quantity that measures the rate at which an object covers distance, defined as the total distance traveled divided by the time taken.

Velocity (v)

Velocity is a vector quantity that measures the rate at which an object changes its position, defined as the displacement divided by the time taken.

Acceleration (a)

The rate at which velocity changes over time (a = Δv / t), measured in m/s².

Sign Conventions for Position and Displacement

East (E) is positive (+), and West (W) is negative (-).

Time Interval Formula (Δt)

Δt = tf - ti (final time minus initial time).

Standard Units for Speed

Meters per second (m/s) or kilometers per hour (km/h).

4 Types of Kinematic Graphs

Distance–Time (How far?), Position–Time (Where?), Speed–Time (How fast?), and Velocity–Time (How fast and which way?).

Slope (Gradient) Formula

The ratio of rise (y-axis) to run (x-axis) on a graph.

Slope of a Distance–Time Graph

Represents the speed of the object (steeper = faster, flatter = slower, horizontal = stopped).

Negative Slope on a Distance–Time Graph

Not possible, because total distance travelled cannot decrease.

Negative Slope on a Position–Time Graph

Possible; it means the object's position is decreasing and it is moving back toward the origin (starting point).

Horizontal Line on a Speed–Time Graph

Means the object is moving at a constant speed.

Positive vs. Negative Slope on a Speed–Time Graph

Positive slope = speed is increasing (constant acceleration); negative slope = speed is decreasing (constant deceleration).

Velocity–Time Graph Horizontal Lines

Above 0 m/s = moving forward at steady speed; At 0 m/s = stopped; Below 0 m/s = moving backward at steady speed.

Velocity–Time Graph Sloping Lines

Sloping upward = speeding up; sloping downward toward 0 = slowing down.

Force (F)

A push, pull, or influence that changes the motion of an object; has both magnitude (measured in Newtons, N) and direction.

Friction Force (Ffriction)

The resistance caused by two objects in contact; it always acts in the opposite direction of motion.

Normal Force (FN)

The support force exerted by a surface on an object; always acts perpendicular to the surface.

Free Body Diagram (FBD)

A diagram showing all external forces acting on a single object, using arrows pointing in the force's direction with lengths proportional to magnitude.

Newton's 1st Law (Law of Inertia)

n object at rest stays at rest, and an object in motion stays in motion at the same speed and direction unless acted upon by an unbalanced force.

Inertia

A property of matter by which an object resists changes in its motion; greater mass means greater inertia.

Balanced vs. Unbalanced Forces

Balanced: equal and opposite forces resulting in Fnet = 0 and no acceleration. Unbalanced: unequal forces causing a net force (Fnet ≠ 0) and acceleration in the direction of the net force.

Newton's 2nd Law

An object with an unbalanced force acting on it will accelerate in the direction of that force (F = m × a).

Newton's 2nd Law Relationships

Acceleration is directly proportional to net force (a ∝ F) and inversely proportional to mass (a ∝ 1/m).

Definition of 1 Newton (N)

1 N = 1 kg·m/s² (the force required to accelerate a 1 kg mass at 1 m/s²)

Newton's 3rd Law (Action–Reaction)

For every action force, there is an equal and opposite reaction force; forces always act in pairs on different objects.

Why Newton's 3rd Law Force Pairs Are Never on the Same FBD

Because action and reaction forces act on two different objects (systems), not on the same object.