The key method to remember is to list what you know, want to know, and don’t know(include signs). For example: if you know \(a, t, x, v_0\) , want to know \(x_0\) and don’t know v, match it to an equation. You would need an equation that doesn’t have v, but has everything else, including \(x_0\). This would match up to equation 2 and solve for \(x_0\).
The next step is to plug in and solve for what you want.
Deciphering the word problem is different for each question, but there are a few hints.
Use the units given to quickly find out what it position, velocity, and acceleration. Ex: \(m/s^2\) is acceleration, while m/s is velocity
Keep in mind the direction for all values
Quickly sketch a graph to visualize the data, or just try to visualize the object in your mind if it is something easy. Ex: a car or human
Piecewise: piecewise functions are basically 2 or more lines combined. Split the lines up and solve them separately. Make separate lists, and you may have to use different equations
Solving 2D Motion:
Break up the initial velocity if it is at an angle
It is always good to solve for time, unless you are given one
This is because time is the same in both directions
Use time to solve for needed variables
Check to see if the problem is ground to ground
This means that the graph is symmetrical to the max height, and at 0.5t, the object is at max height
Look for peak heights
Launching at complementary angles yield the same range/\(\Delta x\)$$ (30 and 60) but have different times
Launching at 45 degrees is the most efficient/largest \(\Delta x\)
Don’t confuse acceleration in free-fall with force of gravity
In freefall- acceleration is always 10 m/s downward
Use dynamics/forces to solve for acceleration if applicable (incline, etc)