Study Notes
Variable acceleration involves understanding how displacement, velocity, and acceleration can change over time and be expressed as functions of time. Calculus, including differentiation and integration, is used to solve kinematics problems and derive constant acceleration formulae.
- Displacement — the distance moved in a particular direction. Example: s = 2t³ - 3t represents displacement as a function of time.
- Velocity — the rate of change of displacement with respect to time. Example: Found by differentiating the displacement function.
- Acceleration — the rate of change of velocity with respect to time. Example: Found by differentiating the velocity function.
- Differentiation — a calculus method to find rates of change. Example: Used to find velocity from displacement.
- Integration — a calculus method to find areas under curves. Example: Used to find displacement from velocity-time graphs.
Exam Tips
Key Definitions to Remember
- Displacement is the distance moved in a specific direction.
- Velocity is the rate of change of displacement.
- Acceleration is the rate of change of velocity.
Common Confusions
- Confusing velocity with speed, which is scalar and does not include direction.
- Mixing up differentiation and integration processes.
Typical Exam Questions
- What is the displacement when t = 2? Substitute t = 2 into the displacement equation.
- How do you find the velocity of a particle at a given time? Differentiate the displacement function with respect to time.
- How can you find the maximum velocity of a particle? Set the derivative of the velocity function to zero and solve for time.
What Examiners Usually Test
- Ability to differentiate and integrate functions of time.
- Understanding of how to apply calculus to solve kinematics problems.
- Derivation and application of constant acceleration formulae.