Physics Study Guide: Motion of Bodies, Speed, Distance, and Time

Motion of a Body: Concepts and Relativity

• Definition of Motion:

  • The motion of a body is defined as the change of its position relative to another body over a certain interval of time.

  • Examples of Motion:

  • A car moving along a road changes its position relative to the road.

  • An airplane in flight changes its position relative to the Earth.

  • A ball flying through the air changes its position relative to the ground.

• Reference Body (Vztažné těleso):

  • The reference body is the specific body relative to which the motion or state of rest of an object is observed and judged.

• Relativity of Motion:

  • Motion is relative, not absolute. The same body can be at rest relative to one reference body while simultaneously being in motion relative to another.

  • Example of Relativity:

  • A passenger sitting inside a moving train is at rest relative to their seat, but is in motion relative to a person standing on the station platform.

Physical Quantities: Distance and Time

• Distance ($s$):

  • Definition: Distance is the total length of the path that a body travels during its motion.

  • Symbol: $s$

  • Basic SI Unit: Meter ($\text{m}$).

  • Other Common Units: Kilometer ($\text{km}$), centimeter ($\text{cm}$), and millimeter ($\text{mm}$).

  • Conversion Factors:

  • $1\,\text{km} = 1000\,\text{m}$

  • $1\,\text{m} = 100\,\text{cm}$

  • Practical Example: If a cyclist travels a distance of $5\,\text{km}$, they have covered a total distance of $5000\,\text{m}$.

• Time ($t$):

  • Definition: Time measures the total duration that the motion lasts.

  • Symbol: $t$

  • Basic SI Unit: Second ($\text{s}$).

  • Other Common Units: Minute ($\text{min}$) and hour ($\text{h}$).

  • Conversion Factors:

  • $1\,\text{min} = 60\,\text{s}$

  • $1\,\text{h} = 60\,\text{min} = 3600\,\text{s}$

Speed and Unit Conversions

• Speed ($v$):

  • Definition: Speed determines the distance a body travels per unit of time.

  • Symbol: $v$

  • Basic SI Unit: Meter per second ($\text{m/s}$).

  • Fundamental Equation:

  • $v = \frac{s}{t}$

  • Where $v$ is speed, $s$ is distance, and $t$ is time.

  • Worked Example:

  • A car travels $100\,\text{m}$ in a duration of $5\,\text{s}$.

  • Calculation: $v = \frac{100\,\text{m}}{5\,\text{s}} = 20\,\text{m/s}$

  • Result: The car moves at a speed of $20\,\text{m/s}$.

• Speed Units and Conversions:

  • In everyday life, kilometer per hour ($\text{km/h}$) is commonly used, whereas meter per second ($\text{m/s}$) is primarily used in physics.

  • Conversion Rules:

  • To convert from $\text{m/s}$ to $\text{km/h}$: multiply the value by $3.6$ ($\text{m/s} \rightarrow \text{km/h}$, multiply by $3.6$).

  • To convert from $\text{km/h}$ to $\text{m/s}$: divide the value by $3.6$ ($\text{km/h} \rightarrow \text{m/s}$, divide by $3.6$).

  • Conversion Examples:

  • Converting $\text{m/s}$ to $\text{km/h}$: $20\,\text{m/s} \times 3.6 = 72\,\text{km/h}$

  • Converting $\text{km/h}$ to $\text{m/s}$: $90\,\text{km/h} \div 3.6 = 25\,\text{m/s}$

Classification of Motion by Speed

• Uniform Motion (Rovnoměrný pohyb):

  • Definition: Motion in which the speed of the body remains unchanged throughout the movement.

  • Key Characteristic: The body covers equal distances in equal intervals of time.

  • Example: A vehicle traveling continuously at a steady speed of $50\,\text{km/h}$.

• Non-uniform Motion (Nerovnoměrný pohyb):

  • Definition: Motion during which the speed of the body changes.

  • Possible Dynamic Behaviors:

  • Accelerating (speeding up / zrychlovat)

  • Decelerating (slowing down / zpomalovat)

  • Changing speed in various arbitrary ways

  • Example: A car pulling away from a traffic light; it starts at a complete stop ($0\,\text{km/h}$) and subsequently increases its speed.

Instantaneous Speed vs. Average Speed

• Instantaneous Speed (Okamžitá rychlost):

  • Definition: The speed of an object measured at a specific, single moment in time.

  • Example: A car speedometer currently indicating $70\,\text{km/h}$ shows its instantaneous speed at that precise instant.

• Average Speed (Průměrná rychlost):

  • Definition: The overall speed evaluated across the complete distance/duration of the motion.

  • Formula:

  • $v = \frac{s}{t}$

  • Worked Example:

  • A cyclist covers a distance of $30\,\text{km}$ in $2\,\text{h}$.

  • Calculation: $v = \frac{30\,\text{km}}{2\,\text{h}} = 15\,\text{km/h}$

  • Result: The cyclist's average speed over the whole trip was $15\,\text{km/h}$.

Calculating Distance and Time

• Algebraic Derivations:

  • From the central relationship $v = \frac{s}{t}$, equations for distance and time are derived:

  • Distance Formula: $s = v \times t$

  • Time Formula: $t = \frac{s}{v}$

• Worked Example for Distance:

  • Problem: A body moves at a speed of $10\,\text{m/s}$ for a duration of $6\,\text{s}$. Calculate the total distance traveled.

  • Calculation: $s = 10\,\text{m/s} \times 6\,\text{s} = 60\,\text{m}$

  • Result: The body covers a distance of $60\,\text{m}$.

Summary of Units and Essential Rules

• Summary of Physical Quantities:

  • Distance ($s$): Measured in meters ($\text{m}$).

  • Time ($t$): Measured in seconds ($\text{s}$).

  • Speed ($v$): Measured in meters per second ($\text{m/s}$).

• Key Formulas:

  • Most important formula: $v = \frac{s}{t}$

  • Derived distance formula: $s = v \times t$

  • Derived time formula: $t = \frac{s}{v}$

• Crucial Rule Before Calculating:

  • Always verify and standardize units before starting any numerical calculation.

  • If calculating speed in $\text{m/s}$, distance must be in meters ($\text{m}$) and time must be in seconds ($\text{s}$).