Kinematics: Motion, Speed, Velocity, Acceleration, Displacement, Scalars & Vectors (copy)

Motion

The change in position of an object with respect to its surroundings in a given interval of time.

Speed

The measure of how fast something is moving; calculated as distance covered over a given time.

Velocity

The speed and direction of motion of an object; calculated as displacement over time.

Acceleration

The rate of change in velocity over time.

Displacement

The change in position of an object, considering direction; a vector quantity.

Distance

The total length of the path traveled by an object; a scalar quantity.

Scalar Quantity

A quantity that is fully described by magnitude only; examples include time, distance, speed.

Vector Quantity

A quantity that has both magnitude and direction; examples include velocity, acceleration, force.

Formula for Speed

$$\text{Speed} = \frac{d}{t}$$

Formula for Velocity

$$\text{Velocity} = \frac{\text{displacement}}{\text{time}} = \frac{\triangle x}{\triangle t}$$

Formula for Acceleration

$$a = \frac{\triangle v}{\triangle t}$$

Formula for Displacement under Constant Velocity

$$\triangle x = v \times t$$

Relationship Between Time, Distance, and Speed

$$t = \frac{d}{s}$$

Net Change in Position

The difference between the initial and final positions of an object, represented by displacement.

Direction of Motion

The line along which an object moves, defining its velocity.

Magnitude

The size or quantity of a vector, representing how much there is of something.

Change in Velocity

The difference between an object's final and initial velocities.