Equations of Motion

• What are the three main types of graphs that can represent motion?

  Displacement-time graphs, velocity-time graphs, and acceleration-time graphs

  
• What is the definition of displacement?


  Displacement is the distance of an object from a fixed point in a specified direction
• What is the difference between scalar and vector quantities?


  Scalar quantities have magnitude only, while vector quantities have both magnitude and direction
• How is velocity defined?


  Velocity is the rate of change of displacement of an object

  
• What does the slope of a displacement-time graph represent?


  The slope of a displacement-time graph represents velocity
• What does a straight diagonal line on a displacement-time graph indicate?


  A straight diagonal line represents a constant velocity
• What does a curved line on a displacement-time graph represent?


  A curved line represents an acceleration
• What does a zero slope on a displacement-time graph indicate?


  A zero slope (horizontal line) represents a state of rest
• What does the area under a velocity-time graph represent?


  The area under the curve equals the displacement or distance travelled

  
• What does the slope of a velocity-time graph represent?


  The slope of a velocity-time graph represents acceleration

  
• What does a straight line on a velocity-time graph indicate?


  A straight line represents uniform acceleration
• What does a zero slope on a velocity-time graph indicate?


  A zero slope (horizontal line) represents motion with constant velocity

  
• What does the y-intercept of a velocity-time graph represent?


  The y-intercept equals the initial velocity
• What does the area under an acceleration-time graph represent?


  The area under the curve equals the change in velocity

  
• What does a zero slope on an acceleration-time graph indicate?


  A zero slope (horizontal line) represents an object undergoing constant acceleration

  
• What is the formula for acceleration?


  Acceleration = change in velocity / time = $\frac{\Delta v}{\Delta t}$
• What does the gradient of a velocity-time graph represent?


  The gradient of a velocity-time graph is equal to the acceleration

  
• What happens to the gradient of a velocity-time graph when acceleration increases?


  When acceleration increases, the gradient of the velocity-time graph increases

  
• What is the significance of the final equation of motion?


  This final equation can be derived from two of the other kinematic equations

  
• What are the four kinematic equations of motion?


  1. \( v = u + at \)
  2. \( s = \frac{1}{2}(u + v)t \)
  3. \( s = ut + \frac{1}{2}at^2 \)
  4. \( v^2 = u^2 + 2as \)

  
• What is the first step in solving problems with kinematic equations?


  Write out the variables that are given in the question, both known and unknown

  
• What should you do after listing the known quantities in a kinematic problem?


  Choose the equation which contains the quantities you have listed
• What is the final step in solving kinematic equations problems?


  Substitute in the values, convert units to SI, and rearrange to determine the answer

  
• What is the significance of the example involving the train and markers?

  It illustrates how to apply kinematic equations to real-world scenarios
• What is the acceleration due to gravity on Earth?


  Approximately $9.81 \, \text{m/s}^2$
• What are the key points to remember about motion graphs?

  • Gradient of displacement-time graph = velocity
  • Gradient of velocity-time graph = acceleration
  • Area under velocity-time graph = displacement
  • Area under acceleration-time graph = change in velocity

  
• What are the steps to derive the kinematic equations of motion?


  1. Start with the definition of acceleration.
  2. Relate velocity and time.
  3. Use average velocity to find displacement.
  4. Combine equations to derive the final equations.

  
• What is the formula for displacement in terms of initial and final velocity?


  Displacement \( s = \frac{1}{2}(u + v)t \)
• What is the formula for displacement when initial velocity is zero?


  Displacement \( s = \frac{1}{2}at^2 \)
• What is the formula for final velocity in terms of initial velocity and acceleration?


  Final velocity \( v = u + at \)

  
• What is the formula for final velocity squared in terms of initial velocity and displacement?


  Final velocity squared \( v^2 = u^2 + 2as \)

  
• Why is it important to remember the kinematic equations for the exam?


  Only two equations are given on the data sheet, so you must remember the others

  
• What is the significance of the acceleration of free fall experiment?


  It aims to determine the acceleration due to gravity in a laboratory setting
• What is the initial velocity \( u \) in the kinematic equation example?


  50 m/s

  
• What is the final velocity \( v \) in the kinematic equation example?


  10 m/s

  
• What is the time \( t \) in the kinematic equation example?


  20 s

  
• What is the equation that links \( u \), \( v \), \( t \), and \( s \)?


  s = \frac{(u + v)}{2} t

  
• If \( u = 50 \, \text{m/s} \), \( v = 10 \, \text{m/s} \), and \( t = 20 \, \text{s} \), what is \( s \)?


  s = 600 m

  
• What is the overall aim of the acceleration of free fall experiment?


  • Calculate the value of the acceleration due to gravity, \( g \)
  • Measure the time it takes for a ball-bearing to fall a certain distance

  
• What is the independent variable in the acceleration of free fall experiment?


  Height, \( h \)