Exam Questions - Linear motion with variable acceleration

Exam Questions - Linear motion with variable acceleration

Understanding Linear Motion with Variable Acceleration

  • In linear motion with variable acceleration, acceleration is not constant but changes with time or displacement.
  • Acceleration can be represented as a function of time (a(t)) or displacement (a(s)).
  • This variable acceleration may occur due to varying forces acting on the moving object.

Using Calculus in Variable Acceleration

  • Calculus, specifically differentiation and integration, is key to solving problems in this area.
  • Since acceleration is the derivative of velocity with respect to time and the second derivative of displacement with respect to time, these relationships can be used to derive equations describing motion.
  • Integration is used when you have acceleration as a function and you are trying to find velocity or displacement.

Example Problem Types

  • You may encounter problems that require you to find displacement, velocity, or time at a specific point given an acceleration function.
  • These may require use of initial conditions, like an initial velocity or displacement, to solve for constants after integrating.
  • Sometimes, acceleration might be expressed as a function of displacement rather than time, requiring a different approach.

Utilising Kinematic Equations

  • Kinematic equations, or SUVAT equations, may be useful in this topic, but can only be applied when acceleration is a simple function of time (usually a polynomial).
  • Remember the definitions: s represents displacement, u the initial velocity, v the final velocity, a the acceleration, and t the time.

Key Strategies and Techniques

  • Identifying whether acceleration is a function of time or displacement is a crucial first step in approaching problems.
  • Mastering how to properly integrate or differentiate the function is a non-negotiable skill for this area.
  • For complex acceleration functions, try to rewrite or simplify them to a more manageable form before integrating or differentiating.
  • Initial conditions in the problem are essential for finding the constant of integration, so always ensure to take them into account.