Kinematics, the study of motion, is one of the more grueling units in any physics course. Often, the curriculum starts out fairly straight forward distinguishing between:
|Scalar quantities||Measurements/values that are never negative||
|Vector quantities||Measurements/values that include direction [usually indicated by a positive or negative (+/-) sign]||
From there, most courses define functions and equations for position, velocity, and acceleration, eventually concluding with the four essential 1-dimensional kinematic formulas:
|vf = v0 + at||vf2 = v02 + 2ad|
|d = v0t + (1/2)at2||d = (1/2)(vf + v0) t|
Note: Some books/teachers use the following conventions instead:
- v(t) in lieu of vf, for instantaneous velocity instead of final velocity
- vi in lieu of v0, for initial velocity
- x(t) or x in lieu of d, for position/distance
While 1-D motion problems may be fairly straightforward, 2-d problems can be a little more math intensive- using algebra and trigonometry, and sometimes Calculus. 2-D projectile motion (also referred to as parabolic motion or parametric equations) often provide some initial conditions, and ask the student to solve for:
- Velocity vector broken into horizontal (x) and vertical (y) components
- Maximum height attained
- Time to reach max height
- Total time in the air
- Total distance (horizontal range) of projectile
- Landing or final impact velocity
- Landing or final impact angle/direction.
2-D projectile motion problems typically represent one of these four types of situations:
Simplify the process and double check 2-D projectile motion and parabolic motion problems with these useful tools!
- Here’s a great tool to input your initial conditions for a 2-d kinematics problem and solve for a variety of variables. It accepts initial conditions as a vector with initial angle, or as individual vector components.