Chapter 2: One-Dimensional Kinematics Section 1: Displacement & Velocity

The displacement of an object does not always equal the distance it has traveled.

Displacement can be either positive or negative…depending on your frame of reference. The right (or east) will be considered positive unless otherwise stated. Likewise with up (north). The left (or west) will be considered negative unless otherwise stated. Likewise with down (south). PositiveNegative ∆ x = 8 cm ∆ x = -4 cm

Why refer to it as average velocity? Example: Suppose you traveled from your house to school…a distance of 4.0 km. It took you.20 hours (12 minutes) because of heavy traffic. Your avg velocity would be: v = 4.0 km /.20 h v = 20 km/h Did you travel at that exact speed for the entire trip? Of course not. Because of this, velocity is an average.

Object 1 Object 2 Object 3 Time Position

So, what does it mean if the position vs. time graph isn’t a straight line?

The velocity at precisely 4 seconds has a special name. It is called the “instantaneous velocity”..

Chapter 2: One-Dimensional Kinematics Section 2: Acceleration

Acceleration is a vector quantity; its magnitude tells how quickly the change is happening.  The sign tells the direction.  Acceleration with a “+” magnitude means the object is gaining velocity in the “+” direction.  Acceleration with a “–” magnitude means the object is slowing down (or gaining velocity in the “–” direction.

Acceleration can be determined using a velocity vs time graph.

Decided whether the following statements are true or false, and justify your choice: 1)A car must always have an acceleration in the same direction as its velocity. 2)It’s possible for a slowing car to have a positive acceleration. 3)An object with constant, nonzero acceleration can never stop and remain at rest.

The slope of a velocity vs. time graph represents average acceleration.

Chapter 2: One-Dimensional Kinematics Section 3: The Kinematic Equations

Displacement with Constant Acceleration: Note that:  This equation does not require acceleration.

Displacement with Constant Acceleration: Note that:  “t” is actually “∆t”.  However, t i is usually 0.  The equation can be rewritten to find x i.

Velocity with Constant Acceleration: Note that:  This equation does not require time.  ∆x = (x f – x i )

All objects free fall with an acceleration of g = -9.8 m/s 2.  You may use the rounded value of 10 m/s. In other words, gravity causes objects to speed up as they fall downward.  It also causes objects to slow as they travel upward.  For objects that are falling, launched, or thrown, downward acceleration is the value of gravity.