IB DP Maths: AA HL复习笔记5.6.2 Calculus for Kinematics
Differentiation for Kinematics
How is differentiation used in kinematics?
- Displacement, velocity and acceleration are related by calculus
- In terms of differentiation and derivatives
- velocity is the rate of change of displacement
If a graph is not given you can use your GDC to draw one
- velocity is the rate of change of displacement
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- you can then use your GDC’s graphing features to find gradients
- velocity is the gradient on a displacement (-time) graph
- acceleration is the gradient on a velocity (-time) graph
- you can then use your GDC’s graphing features to find gradients
Worked Example
Integration for Kinematics
How is integration used in kinematics?
How would I find the constant of integration in kinematics problems?
- A boundary or initial condition would need to be known
you might also be given information about the object at some other time (this is called a boundary condition)- substituting the values in from the initial or boundary condition would allow the constant of integration to be found
How are definite integrals used in kinematics?
Exam Tip
- Sketching the velocity-time graph can help you visualise the distances travelled using areas between the graph and the horizontal axis
Worked Example
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