Kinematics Cheat Sheet
Kinematics describes motion without considering its causes, focusing on displacement, velocity, acceleration, and time.
Core Principles
- Uniform motion: Velocity is constant, so acceleration is zero.
- Uniformly accelerated motion: Acceleration is constant, allowing for predictable changes in velocity and position over time.
- Free fall: The only force acting is gravity, resulting in a constant downward acceleration (g ≈ 9.8 m/s²).
Action Steps
- 1. Identify known variables (initial velocity, final velocity, acceleration, time, displacement).
- 2. Determine the unknown variable you need to solve for.
- 3. Select the appropriate kinematic equation that relates the knowns and the unknown.
- 4. Substitute the known values into the equation.
- 5. Solve for the unknown variable, ensuring correct units.
Formulas
- Displacement with constant velocity: $\Delta x = v t$
- Final velocity with constant acceleration: $v_f = v_i + a t$
- Displacement with constant acceleration: $\Delta x = v_i t + \frac{1}{2} a t^2$
- Final velocity squared with constant acceleration: $v_f^2 = v_i^2 + 2 a \Delta x$
- Displacement with constant acceleration (alternative): $\Delta x = \frac{v_i + v_f}{2} t$
- Acceleration due to gravity: $g \approx 9.8 \text{ m/s}^2$
Key Terms
- Displacement: The change in position of an object; a vector quantity.
- Velocity: The rate of change of displacement; a vector quantity.
- Acceleration: The rate of change of velocity; a vector quantity.
- Free Fall: Motion under the sole influence of gravity.
Real World Examples
- A car accelerating from rest.: Use kinematic equations to calculate its speed after a certain time or distance.
- An object thrown vertically upwards.: Analyze its motion using kinematic equations, considering gravity as constant acceleration.
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