Motion

• Vectors


  Drawn using arrows of different sizes to show their magnitude, the head of the vector always points in the direction that the vector is travelling, or applied
• Sign convention for vectors


  When adding numbers together on a calculator it is easy to type in "12+5-3", but it is not easy to type in "12 then 5 up and 3 down". For this reason we need to establish a sign convention when dealing with vectors. In 1 dimension (on a line) we establish a consistent direction convention: All vector quantities that we include in our description or diagram must follow the same convention. It is possible to use a different convention in a diagram for a specific reason, but you must include a key showing the convention used and apply the convention consistently.
• Describing a vector


  1. Step 1: Identify the magnitude and unit

  2. Step 2: Identify the direction according to the given convention

  3. Step 3: Combine the magnitude, direction, and unit
• Adding vectors graphically


  Draw the vectors to scale and place head to tail
• Adding vectors algebraically


  Treat 1 dimensional vectors as though they are simply numbers on a number line
• Adding vectors algebraically


  • A student walks 25 m west, 16 m east, 44 m west, and then 12 m east. Use the sign convention shown to add their displacement vectors algebraically. Answer: -25 + 16 - 44 + 12 = -41. Using the sign convention shown, the final answer is the vector 41 m west or -41 m.
• Vector quantity


  Requires both a direction and a magnitude
• Scalar quantity


  Requires only a magnitude to quantify its measurement
• Vector quantities


  • Distance
  • Displacement
  • Velocity
  • Time
• Scalar quantities


  • Distance
  • Time
  • Speed
• Displacement


  The change in position of an object
• Distance


  The total length of the path travelled by an object
• Average speed or velocity


  s is the displacement of the object in metres, t is the time taken for the change in displacement
• Converting units


  You can change between ms-1 and km/hr by a conversion factor of 3.6
• Calculating speed


  • A person measures that a car covers a distance of 100m in 4.2s. Speed = distance/ time = 100/4.2 = 23.8 m/s. Convert to km/hr Speed = 23.8 x 3.6 = 85.7 km/hr
• Calculating time


  • An annoying year 9 student says to his parents on a long car trip, "when are we getting there?". If the trip is 145km and the average speed of the car is 90km/hr, how long will the trip take. T=D/S = 145/90 = 1.61 hours.
• Bearing


  The angle a vector makes when taken clockwise from Due North
• Average speed


  Distance / time
• Average velocity


  Displacement / time
• Adding vectors graphically


  Draw a vector diagram
• Adding vectors graphically


  • A person walks 20km east and then walks 40 km west
  • An ant walks 40cm to the right stops and then continues 30cm to the right
• Distance is the total length of the path travelled by an object, displacement is the change in position of an object
• Quantities


  • Time
  • Distance
  • Displacement
  • Force
  • Speed
  • Velocity
  • Energy
• Calculating time for a marathon


  A marathon runner has a average speed of 5.1 m/s. Time = Distance / Speed = 42km / 5.1 m/s = 8235 s = 2 hours 17 minutes
• Bearings


  • Bearing 60°
  • Bearing 75°
• Calculating average speed and velocity


  For a typical trip to school in the morning
• Calculating average speed and velocity

  A plane travels north for 2000 km in 4 hours and then heads west for 3000 km in 6 hours
• Distance-time graph


  The gradient of the graph is equal to the speed of the object
• Displacement-time graph


  The solid line represents the motion of an object
• Describing motion from a displacement-time graph


  Describe the motion of the object
• Calculating average speed and comparing to gradient


  From a displacement-time graph
• Displacement-time graphs represent the motion of an object
• The gradient of a distance-time graph is equal to the speed of the object
• The solid line on a displacement-time graph represents the motion of an object
• The shaded area under a velocity-time graph represents the distance travelled during the time interval
• Uniform speed or velocity

  The average speed is equal to the speed at any instant, the instantaneous speed is always equal to the average speed
• Non-uniform speed or accelerated motion


  The speed changes over time, the acceleration is equal to the change in velocity over time
• Describing motion from a speed-time graph


  Identify periods of constant speed, acceleration, and deceleration
• The velocity of an object travelling in the opposite direction to another object is represented by a negative value on a speed-time graph
• The average speed is given by (initial velocity + final velocity)/2 for non-uniform motion