Physical Quantities and Free-Falling Bodies

Preliminaries

  • Greetings
  • Attendance
  • Reminders / Announcements

Recap

  • Aristotle believed that heavier objects fall faster.
  • Terrestrial is the movement of the object in the Earth.
  • Celestial is the movement of the objects beyond the Earth.
  • Natural is the motion caused by equilibrium.
  • Violent is the motion caused by external force.
  • Voluntary is the willful movement of humans and animals.
  • Aristotle believed that heavier objects fall faster
  • Galileo dropped weights in Leaning Tower of Pisa to test Aristotle’s Hypothesis.
  • Galileo observed that an object and another object twice as heavy will fall at the same time.
  • The opposing motion that makes a moving object stop is called Friction.
  • Inertia is the property of an object to resist change in motion.

Objectives

  • Recall basic descriptors of motion (distance, displacement, time, speed, velocity, and acceleration);
  • Explain what is meant by the acceleration due to gravity;
  • Solve word problems related to free-falling bodies; and
  • Apply free fall on scenarios that are relevant to daily living.

Is Edward in Motion or Not?

  • Edward stands inside the LRT, holding onto the handrail as the train starts moving. He feels a slight backward pull as it accelerates, the wheels humming against the tracks. When the train slows down suddenly, he leans forward slightly, gripping the rail tighter to keep his balance. Outside the window, buildings and roads blur past as the train speeds up again.

Motion

  • When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object.
  • Motion is simply the movement of an object from one position to another with time.
  • The ideas of Aristotle and Galileo Galilei regarding motion were purely qualitative.
  • These concepts came MOSTLY from thorough observations.

Physical Quantities

  • Physical Quantities are defined as properties of a material or system that can be quantified by measurement.

Physical Quantities, SI Unit, Symbol

  • Length: metre, m
  • Mass: kilogram, Kg
  • Time: Second, S
  • Temperature: Kelvin, K
  • Current: Ampere, A
  • Amount of light: Candela, Cd
  • Amount of substance: mole, Mol

Scalar Quantities

  • Scalar quantities are quantities described with numerical values or magnitude only.
  • Often represented by the normal letters, or in some cases they are italicized (m for mass).
  • Examples: Time, speed, mass, temperature.

Vector Quantities

  • Vector quantities are quantities described with numerical values and direction.
  • Always denoted with an arrowhead on top of their symbols or bold face letters (ex; F for force).
  • Examples: Velocity, Acceleration, Force, Weight

Take Note:

  • Positive (+) is north; east; up; to the right
  • Negative ( - ) is south; west; down; to the left

Distance and Displacement

  • Distance: total length of the path traveled, following all the turns and/or changes in direction.
  • Displacement: straight line path from the starting point directly to the ending point, including the direction of the travel.
  • Both are symbolized by a small letter “d” and the SI unit is meters (m).

Speed, Velocity, and Acceleration

Speed

  • Galileo described speed as the distance covered per unit time.
  • s = d/t
    • s = speed (m/s)
    • d = distance (m)
    • t = time (s)
  • Any of the following combinations of units for distance and time are acceptable:
    • miles per hour (mi/h)
    • meters per second (m/s)
    • kilometers per hour (km/h)
    • centimeters per day
    • light-years per century

Speed Problem:

  • A bus travels 1,000 meters going to the market. The trip takes 200 seconds. What is the speed?
    • Given: d= 1,000m, t= 200 s
    • Required: Speed
    • Equation: s=d/t
    • Solution: s = 1,000m / 200s
    • Answer: The speed is 5 m/s

Velocity

  • The speed and direction of the motion of an object is called velocity.
  • v = d / t
    • v = velocity (m/s + direction)
    • d = displacement (m)
    • t = time (s)

Velocity Problem:

  • A student has a displacement of 304 m north in 180 s. What was the student's average velocity?
    • Given: d= 304 m north, t= 180 s
    • Required: Velocity
    • Equation: v=d/t
    • Solution: s = 304 m / 180s
    • Answer: The velocity is 1.69 m/s, north.

Acceleration

  • When the velocity of an object changes, either due to a change in speed, direction, or both, it is called acceleration.
  • a = ∆v / t
    • a = acceleration (m/s^2 + direction)
    • ∆v = change in velocity (m/s + direction)
    • t = time traveled (s)

Acceleration Problem:

  • A toy car accelerates from 3 m/s to 5 m/s in 5 s. What is its acceleration?
    • Given: Vi= 3m/s ; Vf= 5 m/s ; t= 5s
    • Required: Acceleration
    • Equation: a = ∆v / t
    • Solution: a = (5m/s - 3m/s) / 5s; a = 2m/s / 5s
    • Answer: The acceleration is 0.4 m/s^2

Kinematics

  • It deals with the analysis of the motion of objects without concern for the forces causing the motion
  • These are different set of equations that include variables for displacement, velocity, acceleration, and time.

Linear

Linear Vertical

  • It is defined as motion in a vertical plane. The motion of free-falling objects is the best example of vertical motion.

Linear Horizontal

  • It is defined as motion in a horizontal plane. The motion of bikes, cars, or other vehicles on roads is the best example of horizontal motion.

Horizontal Kinematics

  • Equation 1: d = ((Vi + Vf)/2) * t (Missing Variable: a)
  • Equation 2: a = (Vf - Vi) / t (Missing Variable: d)
  • Equation 3: d = Vit + (1/2)a*t^2 (Missing Variable: Vf)
  • Equation 4: Vf = a*t + Vi (Missing Variable: d)
  • Equation 5: Vf^2 = Vi^2 + 2ad (Missing Variable: t)

Sample Problem

  • Steadily increasing your velocity from 30 km/h to 60 km/h in 5 mins, how much distance can you cover? What is your acceleration?

    • Given: Vi = 30 km/h, Vf = 60 km/h, Time = 5 mins -> 0.08333 hours
    • Required: Distance = ?, Acceleration = ?
    • Equation:
      • Distance: d = ((vi + vf) / 2) * t
      • Acceleration: a = (vf - vi) / t
    • Solution:
      • Distance: d = ((30 (km/h) + 60 (km/h)) / 2) * 0.08333 h
      • Acceleration: a = (60 (km/h) - 30 (km/h)) / 0.08333 h
    • Answer:
      • Distance = 3.75 km
      • Acceleration = 360.01 km/h^2

  • Ferrari LaFerrari can achieve average accelerations of 26.0 m/s^2. Suppose such a race car accelerates from a speed of 20 m/s at a rate of 5.56 s, how far does it travel in this time?

    • Given: a = 26.0 m/s^2, V_i = 20 m/s, time = 5.56 s
    • Required: Distance = ?
    • Equation: Distance: d = v_it + (1/2)a*t^2
    • Solution: d = (20 (m/s)) * (5.56 s) + (1/2) * (26.0 (m/s^2)) * (5.56 s)^2
    • Answer: Distance = 513.08 m

Assignment

  • An airplane at rest accelerates on a runway at 5.50 m/s^2 for 20.25s until it finally takes off the ground. What is the distance covered before take-off?

Announcement

  • Written Work #4
  • WHEN: March 27 & 28, 2025
  • COVERAGE: Lesson 11 – Lesson 13
  • Note: Please wait for further instructions in Canvas.