Further Kinematics

Further Kinematics

Principles of Kinematics

• Kinematics is a branch of mechanics that describes the motion of points, bodies, and systems of bodies without considering how that motion is caused.
• In one-dimensional motion, it’s important to understand the displacement (distance from the initial position), velocity (rate of change of displacement), and acceleration (rate of change of velocity).

Graphical Interpretation of Kinematics

• Graphs are immensely helpful in interpreting kinematic situations. Both velocity-time graphs and displacement-time graphs can provide extensive information about an object’s motion.
• The gradient of a displacement-time graph gives the velocity.
• The gradient of a velocity-time graph gives the acceleration.
• The area under a velocity-time graph gives the displacement.

Kinematic Equations

• Needless to say, study of kinematics relies heavily on using the right kinematic equations.
• There are four basic kinematic equations, each combines one of initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s).

Variable Acceleration

• Situations with variable acceleration can sometimes be solved by using calculus.
• The derivative of displacement with respect to time gives velocity; the derivative of velocity gives acceleration. Conversely, acceleration can be integrated to find velocity, and velocity can be integrated to find displacement.

Numerical Solutions

• Numerical solutions to problems, such as approximating values when something does not move in a straight line or with constant acceleration, also play a key role in further kinematics. Understanding the different approximation methods, like Euler’s method, is critical.