Educator

One Dimensional Kinematics

• Kinematics is the study of motion and how to mathematically describe it (without concern for the forces causing it).
• Position is a location. It is up to us to assign a coordinate system.
• Distance is a measurement of length. We can talk about the distance between two points or the distance traveled. Notice that these aren't always the same thing.
• Displacement is the change between start and end points. While distance is always positive, displacement can be negative.
• Speed is how fast something moves. The distance it travels divided by the time involved.
• Velocity is speed along with a direction. It is the displacement of an object divided by the time involved. While speed is always positive, velocity can be negative.
• Acceleration is the rate at which a velocity changes. The change in velocity divided by the time involved.
• Delta: We use the Greek capital letter delta (∆) to indicate "change in." We can talk about change in velocity as ∆v = v_f − v_i.
• Now that we have delta, we can express velocity as v = [(∆d)/t] and acceleration as a = [(∆v)/t].
• Gravity is a constant acceleration on Earth, always pointing down. Because of this, we make it negative: g=−9.8 [(m/s)/s].
• The most important formula for kinematics connects all these ideas together: d(t) = [1/2] a t² + v_i t + d_i.
• Another formula allows us to connect final velocity and initial velocity without needing time: v_f ² = v_i ² + 2a(∆d).