IB DP Maths: AA HL復習筆記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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