Fundamental Concepts of Motion in Physics

Key Kinematics Concepts

Reference System

A reference system is a coordinate system (O, X, Y) combined with a clock, used to define the position and motion of objects.

Position

Position is the location of a body in space, defined by coordinates within a chosen reference system.

Trajectory

The trajectory is the imaginary path or line described by a moving body, formed by the sequence of positions it occupies over time.

Distance Traveled (Path Length)

Distance traveled (or path length) is the total length of the path covered by a body along its trajectory.

Displacement

Displacement is the vector difference between a body's final and initial positions, indicating the change in position and direction. It is measured in meters (m).

Velocity

Velocity is a vector quantity representing the rate of change of position over time. Its standard international unit is meters per second (m/s).

• Average Velocity: The total displacement divided by the total time taken.
• Instantaneous Velocity: The velocity of a body at a specific moment in time or at a particular point on its trajectory.

Acceleration

Acceleration is the rate at which the velocity of a body changes over time.

• Average Acceleration: The change in velocity divided by the time interval over which the change occurs.
• Instantaneous Acceleration: The acceleration of a body at a specific moment in time or at a particular point on its trajectory.

Types of Motion

Uniform Rectilinear Motion (URM)

Uniform Rectilinear Motion (URM) is characterized by movement along a straight line with constant speed and direction, meaning the acceleration is zero.

Formulas for URM:

• Position: X = X0 + vT
• Displacement: ΔX = vT

Uniformly Accelerated Rectilinear Motion (UARM)

Uniformly Accelerated Rectilinear Motion (UARM) occurs when a body moves along a straight path with constant acceleration.

Formulas for UARM:

• Acceleration: A = (Vf - V0) / T
• Final Velocity: Vf = V0 + AT
• Position: X = X0 + V0T + 1/2 AT2
• Final Velocity Squared: Vf2 = V02 + 2AX

Circular Motion

Circular Motion is the motion of a body whose trajectory describes a circle, covering equal arcs in equal time intervals (for uniform circular motion).

Kinematics Problems

1. Two cars are separated by a distance of 450 km between two cities. The first car travels at 90 km/h, and the second car travels at 100 km/h, moving towards the first. How long will it take for them to meet? What distance will the first car have traveled?

2. At 9:00 AM, a motorist passes a mileage post at 80 km/h. Ten minutes later, a police car passes the same point in pursuit at 105 km/h. How long will it take the police car to catch up? What distance will they have traveled?

3. A traveler arrives late at the port and misses the ship. The ship departed an hour ago and is sailing at 40 km/h. The traveler does not give up and hires a boat sailing at 60 km/h. What distance will the boat travel to catch the ship? How much time will be needed for this?