Kinematics
Table of Contents
Methods
Inspection
- using ordered pairs and the definitions of displacement, velocity, acceleration, and time to analyze motion.
- On position x-time, velocity-time, and acceleration-time graphs.
- only used for straight line simple graph.
- All x-time graphs must be positive.
Slope
- Velocity of the object can be determined from the graph using slope:
- Note: The ratio that defines average velocity also defines the slope of the x-t graph.
- Note: The slope of a velocity time graph gives the acceleration.
Area under the curve
- If the question is asking how far or something in a given interval.
Motion in a Straight Line
Uniform Motion
- Simplest type of motion.
- Velocity is constant.
- Acceleration is zero. \(A = 0\)
- Instantaneous Velocity is equal to average velocity. \(V_I = V_a\)
- Its displacement \(d_x\) may be obtained by multiplying its constant velocity v by the time.
Formula: \(d_x = vt\)
Accelerated Motion
- Velocity is changing.
Uniformly Accelerated Motion
- Velocity is changing at constant rate.
- Acceleration is constant.
- If an object changes its velocity from an initial velocity \(v_i\), and a final velocity \(v_f\), during a time interval \(t\), its acceleration is given by:
Formula:
\begin{equation*} a = \frac{v_f - v_i}{t} \end{equation*}Kinematics Equations
\begin{equation*}
\begin{split}
v_f & = v_i + a\Delta t,\ \text{(no }\Delta x \text{)} \\
\Delta x & = v_{i}\Delta t + \frac{1}{2}a\Delta t^2,\ \text{(no }v_f \text{)}\\
\Delta x & = \left(\frac{v_i + v_f}{2}\right)\Delta t,\ \text{(no a)}\\
\Delta x & = v_f \Delta t - \frac{a\Delta t^2}{2},\ \text{(no }v_i\text{)} \\
2a\Delta x & = v_{f}^{2} - v_{i}^{2},\ \text{(no }\Delta t \text{)}
\end{split}
\end{equation*}