Kinematics and Motion in One Dimension

Position, Velocity, and Acceleration

Kinematics is the study of how objects move, focusing on concepts such as position, velocity, and acceleration. These quantities can be positive, zero, or negative, depending on the chosen reference direction.

• Position: Describes the location of an object relative to a reference point.

• Velocity: The rate of change of position with respect to time. It can be positive or negative, indicating direction.

• Acceleration: The rate of change of velocity with respect to time. It also has direction and can be positive or negative.

Velocity and speed are not always the same; velocity includes direction, while speed is the magnitude only. The slope of a position vs. time graph gives velocity, and the slope of a velocity vs. time graph gives acceleration.

• Instantaneous Velocity: The velocity at a specific moment in time.

• Average Velocity: Calculated over a time interval as the total displacement divided by the total time.

Equation for average velocity:

Equation for acceleration:

Kinematic Equations (Constant Acceleration)

Kinematic equations are used when acceleration is constant. They relate displacement, initial velocity, final velocity, acceleration, and time.

These equations are only valid for constant acceleration scenarios.

Vectors and Vector Addition

Vector Quantities

Vectors have both magnitude and direction. Examples include displacement, velocity, and acceleration. Scalars have only magnitude (e.g., distance, speed).

• Adding Vectors: Place the tail of one vector at the head of another (tip-to-tail method).

• Resultant Vector: The sum of two or more vectors.

• Components: Vectors can be broken into x and y components, which are added separately.

To find the magnitude of the resultant vector:

To find the direction (angle θ):

Every vector must have a direction and magnitude. The sum of scalar magnitudes is not the same as vector addition.

Projectile Motion

Independence of Motion

Projectile motion involves objects moving under the influence of gravity only. The horizontal and vertical motions are independent of each other.

• Horizontal Motion: Constant velocity (no acceleration if air resistance is neglected).

• Vertical Motion: Constant acceleration due to gravity ( downward).

Key points:

• Horizontal velocity does not change during flight.

• Vertical velocity changes due to gravity.

• At the top of the trajectory, vertical velocity is zero.

Equations for projectile motion:

• Horizontal displacement:

• Vertical displacement:

Remember to resolve the initial velocity into horizontal and vertical components:

Frames of Reference

Relative Motion

Motion is always described relative to a chosen frame of reference. The observer's frame determines how motion is measured and described. The 'zero' position and 'zero' velocity are defined by the chosen reference frame.

• Example: If two objects are thrown, their acceleration due to gravity is the same, but their velocities may differ depending on the initial conditions.

Summary Table: Kinematic Quantities

Additional info: Some explanations and equations have been expanded for clarity and completeness, based on standard introductory physics with calculus curriculum.