3.10: Kinematic Equations: Problem Solving
When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two equations to be solved simultaneously to derive the value of the unknown.
In complex problems, it is not always possible to identify the unknowns or the order in which they should be calculated. In such scenarios, it is useful to make a list of unknowns and draw a sketch of the problem to identify the directions of motion of an object. To solve the problem, substitute the knowns along with their units into the appropriate equation. This step provides a numerical answer, and also provides a check on units that can help find errors. If the units are incorrect, then an error has been made. However, correct units do not necessarily guarantee that the numerical part of the answer is also correct.
The final step in solving problems is to check the answer to see if it is reasonable. This final step is crucial as the goal of physics is to describe nature accurately. To see if the answer is reasonable, check both its magnitude and its sign, in addition to its units. This enables us to get a conceptual understanding of the problems that are being solved. Sometimes the physical principle may be applied correctly to solve the numerical problem, but produces an unreasonable result. For example, if an athlete starting a foot race accelerates at 0.4 m/s² for 100 seconds, their final speed will be 40 m/s (about 150 km/h). This result is unreasonable because a person cannot run at such a high speed for 100 seconds. Here, the physics is correct in a sense, but there is more to describing nature than just manipulating equations correctly.
This text is adapted from Openstax, University Physics Volume 1, Section 3.4: Motion with Constant Acceleration.
