IB DP Maths: AA HL复习笔记5.6.1 Kinematics Toolkit

What is kinematics?

• Kinematics is the branch of mathematics that models and analyses the motion of objects
• Common words such as distance, speed and acceleration are used in kinematics but are used according to their technical definition

What definitions do I need to be aware of?

• Firstly, only motion of an object in a straight line is considered
  • this could be a horizontal straight line
    • the positive direction would be to the right
  • or this could be a vertical straight line
    • the positive direction would be upwards

Particle

• A particle is the general term for an object
  • some questions may use a specific object such as a car or a ball

Are there any other words or phrases in kinematics I should know?

• Certain words and phrases can imply values or directions in kinematicsWhat are the key features of a velocity-time graph?

• The gradient of the graph equals the acceleration  of an object
• A straight line shows that the object is accelerating at a constant rate
• A horizontal line shows that the object is moving at a constant velocity
• The area between graph and the x-axis tells us the change in displacement of the object
  • Graph above the x-axis means the object is moving forwards
  • Graph below the x-axis means the object is moving backwards

   

• The total displacement of the object from its starting point is the sum of the areas above the x-axis minus the sum of the areas below the x-axis
• The total distance travelled by the object is the sum of all the areas
• If the graph touches the x-axis then the object is stationary at that time
• If the graph is above the x-axis then the object has positive velocity and is travelling forwards
• If the graph is below the x-axis then the object has negative velocity and is travelling backwards