forces and motion

• Speed


  A scalar quantity that only has a magnitude (size or extent)
• Velocity


  A vector quantity that has both a magnitude and a direction
• Speed vs Velocity


  Speed only has magnitude, velocity has both magnitude and direction
• Distance


  A scalar quantity that only has a magnitude
• Displacement


  A vector quantity that has both a magnitude and a direction
• Calculating speed


  Distance / Time
• Calculating velocity


  Displacement / Time
• People often use the velocity equation even when they don't have a direction</b>
• The benefit of using velocity is that you can have a negative velocity to represent going backwards
• Objects often don't move at a constant speed but vary along their journey
• Calculating average speed/velocity


  Total distance or displacement / Total time
• Real life speeds in meters per second


  • Walking: 1.5
  • Running: 3
  • Cycling: 6
  • Car on main road: 25
  • Fast train: 55
  • Plane: over 250
• Sound waves travel at 330 meters per second in air
• The speed of sound waves changes when traveling through different mediums like water
• Wind speed can vary from almost 0 to faster than a speeding train, affected by temperature, atmospheric pressure, and structures
• Acceleration


  The rate of change in velocity or how quickly something speeds up or slows down
• Acceleration


  • Measured in meters per second squared
• Delta (Δ)


  Means change
• Delta v (Δv)


  Change in velocity, can also be written as v - u where v is final velocity and u is initial velocity
• Calculating acceleration


  1. Find change in velocity (v - u)

  2. Divide by time
• Acceleration is a vector quantity, so it has direction as well as magnitude and can be negative (implying slowing down or decelerating)
• Acceleration calculated is the average acceleration over the time period, as it may have varied
• Uniform/constant acceleration


  Acceleration is the same rate the entire time
• Second acceleration equation


  • Includes distance (s) instead of time (t)
• If an object starts from stationary, its initial velocity (u) is zero
• Ball dropped from unknown height

  • Final velocity (v) is 7 m/s
  • Initial velocity (u) is 0 m/s
  • Acceleration due to gravity is 9.8 m/s^2
• Calculating height dropped


  1. Rearrange equation to solve for distance (s)

  2. Plug in values for v, u, and a
• Distance-time graphs


  Allow us to visualize how far something has traveled in a certain period of time
• Distance-time graphs


  • Tell us a lot about the different parts of the journey
  • We need to be able to interpret each of these different stages
• Gradient of the line

  Tells you the speed that the object is traveling at that time
• Gradient of the line

  Is equal to the change in distance divided by the change in time, which is the formula for speed
• Interpreting a distance-time graph


  1. For a straight line section: Calculate the gradient to find the constant speed

  2. For a flat line: The gradient and speed are both zero, meaning the object is stationary

  3. For a curved line: The speed is constantly changing, so we need to draw a tangent to find the speed at a particular point
• To find the speed at a particular point on a curved line, we need to draw a tangent to the curve at that point and calculate the gradient of the tangent
• Straight lines represent constant speeds, flat lines mean stationary, and curved lines represent changing speeds
• Velocity-time graph


  Graph that shows how an object's velocity changes over time
• Velocity-time graph


  Similar to distance-time graph, but with velocity on y-axis and time on x-axis
• It's easy to confuse velocity-time and distance-time graphs in exams, so be careful to check which one you're looking at
• Gradient of velocity-time graph


  Change in velocity over change in time, which is the formula for acceleration
• Constant positive gradient on velocity-time graph

  Constant acceleration
• Constant negative gradient on velocity-time graph

  Constant deceleration