Physics Chapter 2: Kinematics

Chapter 2: Kinematics

• Kinematics is the study of motion without considering the cause.
• It describes how things move.
• For example, the heart moving blood through veins while you rest is an example of kinematics.

Warm-up Session

• The father of the scientific method is Galileo Galilei.

Significant Figures

• The number of significant figures in 0.005 is 1.

Vectors vs Scalars

• Scalars have only magnitude.
• Vectors have both magnitude and direction.
• Vectors are represented by arrows.
• Vectors can be one-dimensional.

Displacement

• Position tells us where an object is at a particular time.
• Distance is a scalar that represents the total distance traveled.
• Displacement is a vector that represents the net change in position.
  • If you run 4 laps around a 400m track, your distance is 1600m, but your displacement is 0m.
• Displacement is the difference between the final and initial positions.
• Δx = xf - xo
  • Δx is displacement
  • xf is the final position
  • xo is the initial position
• If direction changes during movement, displacement is less than distance traveled.
• A professor pacing left and right across a 3.5 m wide whiteboard will have a displacement of +2 m to the right depending on initial position.

Displacement Calculation Example

• If initial position is 2m and final position is 4.5m to the right, the displacement is 2.5 m.

Distance

• Distance is the magnitude of displacements between two positions.
• It's the total length of the path traveled between two positions.
• Distance has no direction.

Speed and Velocity

• Speed is a scalar, calculated as total distance divided by time.
  • Speed = distance / time
• Velocity is a vector that has magnitude and direction.
  • Average velocity = displacement / elapsed time
  • Δx / Δt = (xf - xo) / (tf - to)

Time, Velocity, and Speed

• The SI unit for time is the second (s).
• The SI unit for speed and velocity is meters per second (m/s), or kilometers per hour (km/h).
• Velocity is a vector quantity, while speed is a scalar quantity.

Average Speed Example

• Megan walks 1100m to the left in 330 s. Her average speed is 3.3 m/s.

Instantaneous Velocity

• Instantaneous velocity is the average velocity over an infinitesimally short time interval.
• v = lim (Δx / Δt) as Δt approaches 0

Acceleration

• Acceleration is the rate of change of velocity.
• a = Δv / Δt
• The SI unit for acceleration is meters per second squared (m/s²).
• Acceleration is a vector quantity.
• Instantaneous acceleration is acceleration at a specific moment in time.
• Deceleration is acceleration opposite to direction of motion.

Acceleration Examples

• A car accelerates from rest to 20 m/s in 10 seconds has an acceleration of 2 m/s².
• A car decelerates from 30 m/s to rest in 10 seconds has an acceleration of -3 m/s².
• A truck accelerating from 15m/s to 45m/s in 5 seconds has an acceleration of 6 m/s².

Kinematic Equations for Constant Acceleration

• Several equations allow for solving motion problems. Note them down correctly:
  • ā = (ν-νο) / t
  • v = vo + at
  • x = xo + vot + 1/2 at²
  • v² = vo² + 2a( x− xo)

Freely Falling Objects

• A freely falling object moves only under the influence of gravity.
• Acceleration due to gravity (g) is approximately 9.80 m/s².
• The kinematic equations apply to freely falling objects.

Dropping/Throwing a Ball Example Problems

• Problems involving a ball dropped or thrown upward from a height, which involve finding time to hit the ground or final velocity/maximum height.

Graphical Representation

• Plots of physical quantities against each other allow us to determine velocity and acceleration.
• The slope of a position-time graph gives velocity.
• The slope of a velocity-time graph gives acceleration.
• The area under a velocity-time graph gives displacement.

Problem Solving Skills

• Steps for solving physics problems:
  • Read the problem carefully. Identify objects, questions, and applicable laws/principles.
  • Draw a diagram showing coordinates.
  • Identify given & inferred quantities. Determine quantities to find.
  • Select equations for solving the desired unknowns.
  • Solve symbolically (using variables).
  • Keep track of significant figures while calculating values.
  • Ensure appropriate accuracy in the final answer.
  • Check the reasonableness of the solution—does it make sense, considering known physical constants and the question?
  • Keep careful track of units.

Explore the fundamentals of kinematics, the study of motion. This quiz covers key concepts such as vectors vs. scalars, significant figures, and displacement. Test your understanding of how objects move and the principles governing their motion.