Describing Motion: Kinematics

• All formulas mentioned are included in the index card

Motion in One Dimension

• Physical quantities are measurable properties of objects or systems.
• Length, mass, and time are expressed using numerical values and units of measurement.
• Kinematics is the branch of classical mechanics describing the motion of points, objects, and systems of groups of objects without reference to the causes of motion.
• Kinematics describes the trajectories of points, lines, and other geometric objects along with their differential properties like velocity and acceleration.
• Kinematics is used in astrophysics for the movements of celestial bodies and in mechanical engineering, robotics, and biomechanics for systems composed of joined parts.
• Kinematic equations calculate the trajectory of particles or objects.
• Physical quantities relevant to the motion of a particle include mass (m), position (p), velocity (v), and acceleration (a).
• Magnitude refers to the size or amount of a quantity and is always a non-negative value, answering "How much?".
• Direction indicates the orientation or path that a quantity is facing.
• A scalar is a quantity with only magnitude, while a vector has both magnitude and direction.
• Position: the location of the object.
• Distance: the total length of the path traveled, regardless of shortest paths available.
• Displacement: the shortest path between two points, regardless of the distance traveled.
• Speed is purely the measurement of how fast something can move in a certain amount of time, without direction.
• Velocity accounts for both the speed and direction of motion of the object.
• Acceleration in motion is the rate at which velocity changes with time, in terms of both speed and direction.
• A point or object moving in a straight line is accelerated if it speeds up or slows down.
• Graphs of motion include the position-time graph and the velocity-time graph.
• Position-time graph shows how far an object has traveled from its starting position at any given time since it started moving.
• Velocity-time graph plots an object's velocity against time, visually representing how an object's velocity changes over time.

Motion in Two Dimensions (Projectile Motion)

• Both stones will actually hit the water at the same time. This phenomenon is a fundamental aspect of projectile motion.
• An object thrown at an angle does not travel in a straight line but follows a curved path known as a parabolic trajectory.
• Horizontal Component: Remains constant throughout the motion.
• Vertical Component: Changes due to the gravitational force acting on the object.
• Gravitational force acts vertically, affecting only the vertical component of the object's velocity.
• As the object travels, the horizontal distance covered remains consistent over equal time intervals, while the vertical distance decreases.
• Vertical velocity decreases until it reaches zero at the maximum height, after which the object begins to descend, and the vertical velocity increases as it falls back down.
• If we reduce the angle of ejection, the horizontal range increases.
• At an angle of 45 degrees, the range is maximized.
• If the angle is increased beyond 45 degrees, the range decreases.
• Independence of components: the horizontal and vertical components of an object's motion are independent of each other.
• The horizontal component's velocity is constant and acceleration is 0 m/s².
• The vertical component's velocity is changing and acceleration is due to gravity (9.8 m/s²).
• Range refers to the horizontal distance a the projectile travels from its launch point to the point where it hits the ground at the same height it was launched from.
• The maximum height is determined by the initial vertical velocity and the acceleration due to gravity.
• Time of flight (the total time the projectile is in the air) is determined by the initial vertical velocity and the acceleration due to gravity.