# Problem Solving

### Identifying Variables in Problem Solving

• First up, recognise the variables mentioned in a given problem. They typically include time, displacement, velocity, and acceleration.
• Sometimes, problems may contain initial conditions like initial displacement, initial velocity or specific durations.

### Applying Appropriate Equations of Motion

• Depending upon the variables identified and their relationship within the problem, choose the appropriate equations of motion.
• For problems with constant acceleration, use the standard equations of motion such as v = u + at, s = ut + 0.5(at^2), and v^2 = u^2 + 2as, where u is initial velocity, v is final velocity, a is acceleration, s is displacement, and t is the time interval.
• For non-uniform acceleration, you may need to integrate or differentiate to establish relationships between acceleration, velocity and displacement.

### Simplifying the Problem Using Calculus

• When dealing with more complex problems, often it’s best to break down the issue into smaller parts that are easier to understand and solve.
• If a problem involves different rates of change it might be necessary to use differential equations.

### Using Graphical Approach

• Depending upon the problem, sometimes a graphical approach might be beneficial.
• Displacement-time graphs, velocity-time graphs, and acceleration-time graphs can help visualise the scenario and provide further insight into the problem.
• The slope of the graph represents the derivative, and the area under the graph denotes the integral.

### Doing Checks Afterwards

• Always remember to double-check your answers for rationality. This can include checking the magnitude and direction of the solution or substituting the solution back into the original equation to ensure it holds.
• Units are another essential aspect that needs to be cross-verified. The units of the solution should make sense with the physical quantity being measured.

In solving Kinematics problems, always remember the core principle - the equations describe motion, and the plots illustrate it. Always keep these basics at the back of your mind when unravelling more intricate issues.