Motion

Motion

1. 1 . For describing motions we use a coordinate system

   • Symbols that help organize information
     • For position we use x
       • xᵢ = initial position
       • xբ= final position

2. 2. Distance and displacement

   • Distance is the length travelled (SI unit: meter)
     • Scalar (only has magnitude)
     • Always positive
   • Displacement (Δx) is the change in position (SI unit: meter)
     • Δx = xբ - xᵢ
     • It can be positive or negative
     • Vector (has magnitude and direction)

3. 3. Speed and Velocity

   • Speed is the rate of motion, it is always positive
     • average speed = distance (m) ------------------------ time (s)
   • Velocity tells us on average how fast something its moving and at which direction (defined by its sign)
     • average velocity = Δx displacement (m) ---------------------------- Δt time (s)

4. 4. Position-Time Graphs

   • When we plot the position data on the y axis and the time data on the x axis
   • A table can be done first, but graphs help us visualize the motion and obtain more data
     • Estimate the position at a time that was not originally pointed
     • Average velocity can be determined by knowing the slope of a straight line on the graph
       • Slope: the rise over its run or change in vertical axis / change in horizontal axis
         • Different slopes represent different types of motion. The steeper the slope, the greater the average speed
         • slope = rise / run or slope = Δx /Δt

5. 5. Equation of motion

   • Position-Time Equation
     • With a constant velocity, as time increases, your position changes by an amount equal to your velocity times the elapsesd time
       • Equation of motio
       • Equation for a straight line: y = mx +b
         • • Equation of motion for constant velocity: xբ = xᵢ + vt
     • Created when position-time graphs intersect, the objects in motion instersect

6. 6. Acceleration

   • Changes in speed and/or direction cause an acceleration. SI units: m/s²
     • Humans are not good at sensing velocity but we do detect acceleration
     • average acceleration: Δv change in velocity (m/s) -------------------------------- Δt time (s)
       • Like velocity, it is also a vector
     • It can be constant (instantaneous and avearage acceleration are the same)
       • The velocity-time graph in this case is a straight line with a slope equal to the acceleration
         • The distance traveled by an object is equal to the area under the curve of its velocity-time graph
   • Speed increases when velocity and acceleration have the same sign. And it decreases when velocity and acceleration have opposite signs
     • vբ = vᵢ + at
   • With constant acceleration we can calculate:
     • .....Velocity-Time Equation..... final velocity = initial velocity + (acceleration) (time) kidjsidjisjdipsa
     • Average Velocity vₐᵥ = ½ · (vᵢ + vբ)
       • Position-Time Equation with Average Velocity xբ = xᵢ + vₐᵥt
         • Combining these equations by substituting "vₐᵥ" with its value: ½ · (vᵢ + vբ) on the second equation, we get:
           • This position and time graph with constant acceleration is parabolic, the sign of the acceleration dtermines its direction
     • Velocity-Postion Equation

7. 7. Newton's Laws

   • 1st Law of inertia: an object moving with constant velocity doesn't its state unless a force causes the change
   • 2. Law of force: acceleration is proportional to force and inversely proportional to the mass in this equation
     • F = m (kg) · a
       • SI Unit: the Newton