1. FOR KINEMATICS CALCULUS

2. IN YOUR SEC 4 MATHEMATICS You will study two new topics: Differentiation Integration Together, these two topics are called “calculus” Knowledge of calculus is not required for O level Physics but understanding it will greatly improve your understanding of Kinematics and besides you need to learn it anyways in Sec 4

3. WHAT IS DIFFERENTIATION? Differentiation refers to two things: Firstly, differentiation = finding the gradient of a graph Secondly, in Physics, you need to know these two relationships: Differentiate Displacement → Velocity Differentiate Velocity → Acceleration

4. WHAT IS DIFFERENTIATION? Hence, the gradient of a displacement-time graph refers to the velocity And, the gradient of a velocity-time graph refers to the acceleration

5. EXAMPLE 1 What is the velocity of the object described by the displacement- time graph below?

6. EXAMPLE 2 What is the acceleration of the object described by the displacement-time graph below?

7. WHAT IS INTEGRATION? Integration is the opposite of differentiation Recall: Differentiate Displacement → Velocity Differentiate Velocity → Acceleration For integration it is: Integrate Velocity → Displacement Integrate Acceleration → Velocity

8. WHAT IS INTEGRATION Recall: differentiation = finding the gradient of a graph For integration, it is integration = finding area under a graph Note: Area “under” graph depends on whether the graph is above or below the horizontal axis!

9. EXAMPLE 3 Find the displacement of the object from t = 0 to t = 10 s

10. EXAMPLE 4 Find the displacement of the object from t = 0 to t = 40 s

11. IN SUMMARY Acceleration Velocity Displacement Differentiate (gradient) Differentiate (gradient) Integrate (area under graph)

12. END OF MATH LESSON =)