kinematics

• u = u0 + at


  
  
• 
  

  The velocity-time equation, where v is final velocity, u0 is initial velocity, a is acceleration, and t is time.
• s = u0t + (1/2)at^2


  
  
• 
  

  The distance-time equation, where s is distance, u0 is initial velocity, a is acceleration, and t is time.
• s = ut + (1/2)at^2


  
  
• Value of Gravity


  
  
• What does the velocity-time graph illustrate in Example 1?

  The motion of a cyclist for a period of 12 seconds
• How long does the cyclist move at a constant speed in Example 1?

  For the first 8 seconds
• What happens to the cyclist's speed after the first 8 seconds in Example 1?

  She decelerates at a constant rate
• How do you find the displacement of the cyclist after 12 seconds?

  By calculating the area under the velocity-time graph
• What is the deceleration of the cyclist between 8s to 12s in Example 1?

  • 1.5 ms^-2
• What does 's' represent in the constant acceleration formulae?

  Displacement
• What does 'u' represent in the constant acceleration formulae?

  Initial velocity
• What does 'v' represent in the constant acceleration formulae?

  Final velocity
• What does 'a' represent in the constant acceleration formulae?

  Acceleration
• What does 't' represent in the constant acceleration formulae?

  Time
• What is the formula to find final velocity in constant acceleration?


  <latex{v = u + at}}</latex>
• What is the formula to find displacement using initial and final velocity?

  <latex{s = \frac{(u + v)}{2} t}</latex>
• What is the formula to find displacement using initial velocity and acceleration?

  <latex{s = ut + \frac{1}{2} at^2}</latex>
• What is the formula to find displacement using final velocity and acceleration?

  <latex{s = vt - \frac{1}{2} at^2}</latex>
• What is the acceleration of a particle moving from A to B in Example 3?

  5 ms^-2
• What is the initial velocity of the particle at A in Example 3?

  3 ms^-1
• What is the final velocity of the particle at B in Example 3?

  18 ms^-1
• How do you find the distance from A to B in Example 3?

  Using the formula <latex{v^2 = u^2 + 2as}}</latex>
• What is the distance from A to B in Example 3?

  31.5 m
• What is the acceleration due to gravity represented as?

  g = 9.8 ms^-2
• What is the effect of air resistance on free falling objects?

  It is ignored in this context
• What are the key points about vertical motion under gravity?

  • Acceleration is constant at g = 9.8 ms^-2
  • Downward motion has positive g value
  • Upward motion has g = -9.8 ms^-2
  • Negative value indicates opposite direction to gravity
• What are the characteristics of displacement-time graphs?

  • Displacement on vertical axis, time on horizontal axis
  • 's' represents displacement in meters
  • 't' represents time in seconds
  • Gradients represent velocity
• What are the characteristics of velocity-time graphs?

  • Velocity on vertical axis, time on horizontal axis
  • 'v' represents velocity in meters per second
  • 't' represents time in seconds
  • Gradients represent acceleration
  • Area under the graph represents distance travelled
• What are the types of motion represented in velocity-time graphs?

  • Stationary: No change in displacement
  • Constant velocity: Displacement increases at a constant rate
  • Accelerating: Displacement increases at a greater rate
• What are the constant acceleration formulae?

  1. <latex{v^2 = u^2 + 2as} />
  2. <latex{s = ut + \frac{1}{2} at^2} />
  3. <latex{s = vt - \frac{1}{2} at^2} />