Physics Fundamentals: Quantities, Vectors, and Motion
What is Physics?
Physics is the science that studies physical phenomena through observation and experimentation. It aims to interpret knowledge of the laws governing these phenomena and derive practical applications.
What is a Quantity?
A quantity is a property that can be measured. Measuring a quantity involves comparing it with another of the same kind, which is taken as the unit.
Magnitude Scale
A magnitude scale is established when a magnitude is defined by the value of its measure or module. Examples include mass, length, time, and volume.
Vector Magnitude
A vector magnitude is defined by its module, direction, and sense. Examples include displacement, velocity, acceleration, and force. A vector is a directed line segment, where a segment is a straight position.
Speed: Average Speed (Scalar Quantity)
Average speed, a scalar quantity, is defined as the distance covered by a mobile unit of time.
Formula: Rm = distance traveled / time spent
Instantaneous Velocity
Instantaneous velocity is a vector quantity indicating the velocity of a body at every moment. It coincides with the velocity averaged over an extremely small time interval (approaching zero). The instantaneous velocity is time-dependent and can be calculated from a velocity-time graph or its velocity equation.
Acceleration: Average Acceleration
Acceleration occurs whenever there is a change in velocity. In straight paths, acceleration results from a change in the speed module. In curved paths, it may be due to a change of direction or a change in the module.
Formula: M = (v – vo) / (t – to)
MRU: Uniform Rectilinear Motion
MRU describes the motion of a mobile object whose path is straight and whose speed is constant (in module, direction, and sense). Therefore, it has no acceleration.
Equation of motion: S = So + v * (t – to)
MRUA: Uniformly Accelerated Rectilinear Motion
MRUA is the movement of a particle whose trajectory is a straight line and whose speed increases uniformly over time. Therefore, acceleration is constant.
Rate equation: V = Vo + a * (t – to)
Position-time equation: S = So + Vo * (t – to) + 1/2 * a * (t – to)^2
The Slope
The slope of a line is the tangent of the angle between the line and the abscissa axis.
Position of a Cell Phone
Indicates the position of a cell phone at each instant. It is a vector quantity.
Starting Position
The starting position is the position of a cell phone at the initial time (t = 0 sec).
Describing Movement
To describe a movement, we need to know:
- The type of path followed by the phone.
- The relationship between position and time.
Displacement
Displacement is the change in position of a mobile object between two instants of time.
Space Travel
Space Travel is a scalar quantity (only has value) equal to the length of the path traveled by the mobile between two instants of time. It is always positive. Only if the path is straight and there is no change of direction, the modulus of the displacement vector coincides with the space covered.
Average Speed (Vector Quantity)
Average speed is a vector quantity indicating the movement performed by a mobile unit of time.
Formula: Vm = (S – So) / (t – to)
Position-Time Graph in MRU
If we represent the position on the vertical axis versus time on the x-axis, we obtain a straight line whose intercept coincides with the initial position (P = So) and whose slope (tangent of the angle between the line and the x-axis) coincides with the value of speed. If the mobile moves to the right, the line slopes upward; if it moves to the left, the line slopes downward.
Velocity-Time Graph in MRU
If we represent the velocity on the vertical axis versus time on the x-axis, we obtain a straight line parallel to the x-axis, indicating that the speed is constant in module.
Graphic Acceleration – Time
If we represent the acceleration on the coordinate axis versus time on the abscissa, we obtain a straight line parallel to the x-axis because the acceleration is constant.
Chart Speed – Time
If we represent the velocity on the coordinate axis versus time on the abscissa, we obtain an ascending line as the speed increases with time.