Applications
There are four kinematic equations that describe the motion of objects without consideration of its causes.
Learning Objectives
Choose which kinematics equation to use in problems in which the initial starting position is equal to zero
Key Takeaways
Key Points
- The four kinematic equations involve five kinematic variables: [latex]\text{d}[/latex], [latex]\text{v}[/latex], [latex]\text{v}_0[/latex], [latex]\text{a}[/latex], and [latex]\text{t}[/latex].
- Each equation contains only four of the five variables and has a different one missing.
- It is important to choose the equation that contains the three known variables and one unknown variable for each specific situation.
Key Terms
- kinematics: The branch of physics concerned with objects in motion.
Kinematics is the branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without consideration of the causes of motion. There are four kinematic equations when the initial starting position is the origin, and the acceleration is constant:
- [latex]\text{v} = \text{v}_0 + \text{at}[/latex]
- [latex]\text{d} = \frac{1}{2}(\text{v}_0 + \text{v})\text{t}[/latex] or alternatively [latex]\text{v}_{\text{average}} = \frac{\text{d}}{\text{t}}[/latex]
- [latex]\text{d} = \text{v}_0\text{t} + (\frac{\text{at}^2}{2})[/latex]
- [latex]\text{v}^2 = \text{v}_0^2 + 2\text{ad}[/latex]
Notice that the four kinematic equations involve five kinematic variables: [latex]\text{d}[/latex], [latex]\text{v}[/latex], [latex]\text{v}_0[/latex], [latex]\text{a}[/latex], and [latex]\text{t}[/latex]. Each of these equations contains only four of the five variables and has a different one missing. This tells us that we need the values of three variables to obtain the value of the fourth and we need to choose the equation that contains the three known variables and one unknown variable for each specific situation.
Here the basic problem solving steps to use these equations:
Step one – Identify exactly what needs to be determined in the problem (identify the unknowns).
Step two – Find an equation or set of equations that can help you solve the problem.
Step three – Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units.
Step four – Check the answer to see if it is reasonable: Does it make sense?
Problem-solving skills are obviously essential to success in a quantitative course in physics. More importantly, the ability to apply broad physical principles, usually represented by equations, to specific situations is a very powerful form of knowledge. It is much more powerful than memorizing a list of facts. Analytical skills and problem-solving abilities can be applied to new situations, whereas a list of facts cannot be made long enough to contain every possible circumstance. Such analytical skills are useful both for solving problems in a physics class and for applying physics in everyday and professional life.
