Kinematics Problems in Math AA SL
Kinematics is the branch of physics that describes the motion of objects., focusing on solving problems involving displacement, velocity, acceleration, and total distance travelled.
Key Relationships
The fundamental relationships in kinematics are:
- Velocity as the rate of change of displacement: $v = \frac{ds}{dt}$
- Acceleration as the rate of change of velocity: $a = \frac{dv}{dt} = \frac{d^2s}{dt^2}$
These equations form the foundation for solving most kinematics problems. Understanding their meaning and how to apply them is crucial.
Displacement and Distance
While often confused, displacement and distance are distinct concepts:
- Displacement is the change in position, represented by a vector.
- Distance is the total length of the path travelled, always a positive scalar.
Calculating Displacement
Displacement from time $t_1$ to $t_2$ is given by the integral of velocity:
$s = \int_{t_1}^{t_2} v(t) dt$
This formula allows us to find the net change in position over a time interval.
Calculating Distance
The total distance travelled between $t_1$ and $t_2$ is given by:
$\text{Distance} = \int_{t_1}^{t_2} |v(t)| dt$
NoteThe absolute value of velocity is used because distance is always positive, regardless of direction.
Speed vs. Velocity
Speed is the magnitude of velocity. While velocity is a vector quantity (having both magnitude and direction), speed is a scalar quantity (having only magnitude).
Common MistakeStudents often confuse speed and velocity. Remember: a constant speed doesn't necessarily mean constant velocity. For example, an object moving in a circle at constant speed has changing velocity due to its changing direction.
Solving Kinematics Problems
When approaching kinematics problems, follow these steps:
