Kinematics (science of motion) Concepts

• Displacement (d) is the distance from a reference point.  Displacement is a vector, meaning it has a magnitude (size) and a direction (often simply positive or negative).
• Distance is how far you travel.  It is a scalar because it has only a size, no direction.
• An object can cover distance while ending up without displacement, if it returns to its starting point at the end of the time interval.
• Average Speed is defined as the change in distance over the change in time.  It is a scalar.
• Average Velocity (v) is defined as the change in displacement over the change in time.  It is a vector because displacement is a vector.  Thus it has a magnitude and a direction.  A shorthand version of this definition is v = d/t
• The slope of a d-t graph is velocity.  If the velocity is constant, the d-t graph is linear ( it has one slope/velocity).
• Average Acceleration (a) is defined as the change in velocity over the change in time.  It is a vector and is the slope of the v-t graph.  A shorthand version of this definition is a =v/t.
• Acceleration is a rate of change of a rate of change.  An object that accelerates at 9.8 m/s² gains 9.8 m/s of velocity for every second it accelerates.
• If the d-t graph is a curve, the object is accelerating.  Curves that we see (in this class) usually fit a power regression or a quadratic regression.  Each term in the regression equation has some physical meaning.
• If the d-t graph is a curve, rather than linear, the slope of a tangent line to the curve is the instantaneous velocity at that point on the graph (the velocity at that moment).
• If the v-t graph is a curve, the acceleration is changing.  The slope of the tangent line is the instantaneous acceleration for this graph.
• A positive acceleration makes something traveling in the positive direction speed up, and an object traveling in the negative direction slows down.  A negative acceleration makes something traveling in the negative direction speed up, and an object traveling in the positive direction slows down.
• Working from the definitions above, we can derive useful equations that describe the motion of objects.
• In a vacuum, all falling objects accelerate at the same rate.  The shorthand for this rate is g (g = 9.8 m/s²).
• Objects accelerate at the same rate on earth b/c even though more massive objects experience a greater pull of earth's gravity (or weight), their mass (or inertia) resists that pull.  Air resistance interferes with this fact in the atmosphere.
• The effect of air resistance is more important as objects have the following characteristics: lighter, more surface area, less aerodynamic shape, moving faster.  We will usually ignore air resistance b/c it makes the math easier, but for more accurate results, it must be included in many cases.