Physic

• Converting Units


  When calculating problems in physics it is very important to have the correct units
• Units


  • Distance/displacement is in metres (m)
  • Time is in seconds (s)
  • Mass is in kilograms (kg)
  • Speed/velocity is in metres per second (m/s)
• ALWAYS check your units before starting a calculation in physics (and chem)
• Converting km/h to m/s

  1. Often the speed/velocity of vehicles is given in km/h

  2. This will usually need to be converted to m/s

  3. https://www.youtube.com/watch?v=xrelaubLUPc

  4. If you want, you can learn the method in the link (& similar videos) to convert it as it shows the reasoning behind the calculation

  5. Shortcut:
• Vector quantity


  Has both a size and a direction
• Scalar quantity


  Has a size, but not a direction
• Distance


  • The measurement of how far an object has travelled to go from one place to another
  • It does not have a direction and covers the entire distance an object moved (therefore it is a scalar quantity)
• Displacement


  • The straight-line distance between the starting and finishing points. "As the crow flies"
  • It has both a magnitude (size) and a direction so therefore is a vector quantity
• Calculating displacement using Pythagoras and trigonometry

  1. When right angle triangles are involved

  2. E.g. a person walks North for 3km, and then East for 4km. What is their displacement?

  3. Magnitude part: a^2 + b^2 = c^2, c = √(a^2 + b^2) = 5km, s = 5km N 53° E

  4. Direction part: tan θ = a/b, θ = 53.0°
• Speed


  • A measure of how quickly something moves
  • Average speed can be calculated as: speed = distance/time
  • An object moves faster when it travels a greater distance in a certain time, or covers a set distance in a shorter time
  • Speed is scalar, so it only has a magnitude, but not a direction
• Calculating speed


  • A dog was running after a ball and ran 100m in 20secs. How fast was the dog running on average?
  • Speed = distance/time = 100m/20s = 5m/s
• Calculating distance and time

  1. Can rearrange the average speed calculation to calculate distance (d) and time (t)

  2. E.g. Trinh rides her bike with a constant speed of 5m/s. It takes her 3mins to get to the milk bar. Calculate how far away it is.

  3. d = speed * time = 5m/s * 180s = 900m
• Solving equations


  • Use the GUESS method:
  • G - givens
  • U - unknowns
  • E - equation
  • S - substitute
  • S - solve
• Instantaneous speed


  • Average speed does not give an indication of how slowly or quickly you might have travelled in a journey.
  • Instantaneous speed gives you the speed at a particular instant.
• Velocity


  • Similar to speed, but they cannot be used interchangeably.
  • It is the rate at which displacement changes.
  • Therefore, it measures how displacement changes with time.
  • It is a vector quantity so it MUST have both a magnitude and a direction
• Distance-time graph


  • You can illustrate an object's motion using a graph
  • Time always goes on the horizontal axis
  • Shows how far an object travels as time progresses
  • A straight line indicates that motion has stopped
  • A line with a steep slope indicates the object is moving faster than a line with a gentle slope
  • The slope is known as the gradient
  • The gradient of a distance-time graph is equivalent to the object's average speed over a time interval.
• Calculating speed from a distance-time graph

  1. Choose two points on the slope

  2. E.g. (4, 80) & (3, 60)

  3. Speed = (80 - 60) / (4 - 3) = 20m/s

  4. It doesn't matter which two points you choose, the gradient will always be the same as long as the slope doesn't change.
• Displacement-time graph


  • Also called position-time graph
  • Shows how far an object has travelled in relation to where it started.
  • Just like a distance-time graph, a steeper slope represents a faster velocity, and a straight line represents a stationary object.
  • If the line goes below zero, it just means the object has moved backwards in relation to its starting position.
  • Can calculate velocity from the gradient of a displacement-time graph
• Calculating velocity from a displacement-time graph


  1. Calculated the same way as speed from a distance-time graph except you need to take in account the position from zero (displacement)

  2. E.g. the velocity for the first 3 seconds is: (6 - 0) / (3 - 0) = -2m/s (in a negative direction)

  3. E.g. the velocity between 3 and 5 seconds is: (12 - 6) / (5 - 3) = 3m/s (in the positive direction)
• Velocity-time graphs


  • Shows how an object's velocity changes over time (can also show speed as long as the object is going in the same direction)
  • An object's velocity may:
  • Be constant, as shown by a flat line
  • Increase, as shown by the graph rising upwards
  • Decrease, as shown by the graph falling downwards
  • The area under a velocity-time graph shows the displacement/distance of the object at that point in time
  • The gradient of a velocity-time graph is the acceleration
• Calculating Displacement from a velocity-time graph

  1. Have to calculate the area of triangles and rectangles and sometimes add them together. (Area of a triangle=½base x height)

  2. Calculate the displacement of the object after it has moved for:

  3. 10secs b) 20secs, c) 30secs, d) 40secs, e) 50secs
• Acceleration


  • The rate of change of velocity or speed over time
  • It can be a vector a scalar depending on whether speed or velocity is being used
  • Units are m/s^2 or ms^-2
  • E.g. acceleration of 9.8m/s^2 means that every second, the object's speed is increasing by 9.8m/s
  • So the object is speeding up. A negative acceleration value means the object is slowing down (deceleration)
• Calculating acceleration


  1. Acceleration equals change in velocity over time

  2. Where Δv = change in velocity, v1 = initial velocity, v2 = final velocity

  3. E.g. If an object travelling at 2m/s speed up to 8m/s and it takes 3 seconds, what is its acceleration?

  4. v1 = 2m/s, v2 = 8m/s, t = 3sec, a=?

  5. a = (v2 - v1)/t = (8 - 2)/3 = 2m/s^2
• Calculating acceleration


  1. If the problem gives you final velocity (v), initial velocity (u) and displacement (s), you can use the following equation to work out acceleration by rearranging the formula:

  2. Another formula that could be used if the relevant information is given is:
• Graphs Summary


  • Step 1: are you looking at a distance/displacement-time graph or a velocity/speed-time graph?
  • The gradient of a displacement/distance-time graph is the velocity/speed
  • The gradient of a velocity/speed-time graph is acceleration
  • The area under the curve of a velocity/speed-time graph is the displacement/distance