# 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.