basics

• Distance


  How far something has traveled
• Displacement


  The difference between the final position and the initial position, including direction
• Distance is a scalar quantity (has magnitude only)
• Displacement is a vector quantity (has magnitude and direction)
• Displacement examples


  • Traveling 8 meters east, then 3 meters west results in a displacement of 5 meters east
• Speed


  How fast something is moving (distance per unit time)
• Velocity


  Speed with direction (a vector quantity)
• Speed is always positive, velocity can be positive or negative
• Average speed is distance divided by time, average velocity is displacement divided by time
• Acceleration


  How fast the speed is changing
• Comparing acceleration of a truck and a sports car


  Sports car has greater acceleration
• Calculating average velocity


  1. Divide net displacement by time

  2. Negative value indicates motion in westward direction
• Acceleration


  How fast the velocity is changing
• Comparing acceleration of a truck and a sports car

  • Truck: 0 to 60 mph in 30 seconds
  • Sports car: 0 to 60 mph in 5 seconds
• Formula for acceleration


  Acceleration = (Final velocity - Initial velocity) / Time
• Calculating acceleration


  • Truck: 60 mph / 30 s = 2 mph/s
  • Sports car: 60 mph / 5 s = 12 mph/s
• Sports car has greater acceleration than truck
• Calculating velocity over time with constant acceleration

  1. Initial velocity

  2. Acceleration

  3. Time

  4. Final velocity = Initial velocity + (Acceleration * Time)
• If acceleration and velocity have the same sign, the object is speeding up. If they have opposite signs, the object is slowing down.
• Gravitational acceleration (g)


  Acceleration due to gravity, -9.8 m/s^2 on Earth
• Gravitational acceleration acts in the vertical (y) direction, not the horizontal (x) direction
• Calculating vertical velocity with gravitational acceleration


  1. Initial vertical velocity

  2. Gravitational acceleration (g = -9.8 m/s^2)

  3. Time

  4. Final vertical velocity = Initial vertical velocity + (g * Time)
• When an object is thrown upward

  Vertical velocity decreases due to negative gravitational acceleration
• Calculating vertical velocity of an upward thrown object

  1. Initial upward vertical velocity

  2. Gravitational acceleration (g = -9.8 m/s^2)

  3. Time

  4. Final vertical velocity = Initial vertical velocity + (g * Time)
• Object reaches maximum height when vertical velocity is zero
• After reaching maximum height, object begins falling downward with negative vertical velocity
• Vertical velocity changes over time

  1. Positive 19.6 two seconds later

  2. Decrease by 9.8 to positive 9.8 three seconds later

  3. Reach zero at maximum height
• Reaching maximum height


  • Vertical velocity is zero, no longer going up or down
• It took three seconds to reach maximum height
• Position A, B, C

  1. When vertical velocity is zero
  2. At maximum height
  3. After maximum height
• Vertical velocity changes after maximum height

  1. Negative 9.8 four seconds later

  2. Negative 19.6 five seconds later

  3. Negative 29.4 six seconds later
• Projectile motion


  Object moving under the influence of gravity
• In typical projectile motion problems, friction is usually ignored
• One-dimensional projectile motion


  Motion in only the y-direction
• Two-dimensional projectile motion


  Motion in both the x and y directions
• Trajectory


  The path the projectile travels
• Velocity components in two-dimensional projectile motion

  Initial horizontal velocity (vx) constant

  Vertical velocity (vy) decreases by 9.8 m/s each second due to gravity
• Acceleration in the horizontal direction (ax) is zero for projectile motion unless stated otherwise
• Velocity in the horizontal direction (vx) is constant for projectile motion unless stated otherwise
• Calculating initial velocity components for two-dimensional projectile motion

  vx = v * cos(theta)

  vy = v * sin(theta)