Notes:Color Guide

Chapter 2: One-Dimensional KinematicsSection 1: Displacement & Velocity

The study of physical concepts such as mass and force is called dynamics.The dynamics of objects in motion is called kinematics.

The motion of an object describes the change of the objects position relative to some reference point.

Objects that are at rest are not in motion.An object undergoes displacement when its position changes.So, displacement is the change of position.

The displacement measures how far an object has moved from its starting location.Note: is the Greek symbol delta. It means a change in. xf means final position. xi means initial position.Displacement: x = xf xiThe displacement of an object does not always equal the distance it has traveled.

Displacement can be either positive or negativedepending 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).

PositiveNegativex = 8 cmx = -4 cm

With your partner, discuss the following:What is this objects position at 1 minute?What is the objects position at 2 minutes?What is its displacement between 1 min and 5 min?Describe the motion of this object.

If we consider the amount of time taken to cause displacement, then we can discuss speed or velocity.The average speed of an object is the length of the path traveled divided by the total amount of time elapsed.

Speed is a scalar quantity. It has a magnitude, but no direction.It is always positive.Average Speed: v = dtThe unit of speed is meters per second: msIf we consider the direction of an objects motion, then we can discuss its velocity.

Velocity is the change of position divided by the change in time.

x = xf xit = tf tiVelocity is a vector quantity, and can be positive or negative, which represents direction.Average Velocity: v = x tThe unit of velocity is meters per second: msWhy refer to it as average velocity?Example:Suppose you traveled from your house to schoola 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 hv = 20 km/hDid you travel at that exact speed for the entire trip? Of course not.Because of this, velocity is an average.(Final) Displacement: xf = vt + xi(For a constant velocity)With your partnerUse the base velocity equation to derive an equation to solve for the final displacement of an object.

Use the equation to answer the following question:A crow flies east in a straight line. It begins flying at 3:04, and comes to a rest at 3:11. It was flying at an average velocity of 1.5 m/s. How far did the crow move from its initial position (in meters)?

630 metersVelocity can be determined using a position vs. time graph. The slope of the line corresponds to the velocity.

Position vs TimeObject 1Object 2Object 3TimePositionHow could we describe the motion of these objects?So, what does it mean if the position vs. time graph isnt a straight line?

With your partnerSketch the graph shown, and draw a straight line that represents the following:The average velocity.The velocity of the object from 0s to 2s.The velocity of the object at precisely 4 seconds.

The velocity at precisely 4 seconds has a special name. It is called the instantaneous velocity..Instantaneous velocity is the slope of the position vs. time curve at a given time.Instantaneous speed is the magnitude of instantaneous velocity.

It can also be said that instantaneous velocity equals the limit of the average velocity as the time interval approaches zero. Or

Chapter 2: One-Dimensional KinematicsSection 2: Acceleration

The change of velocity over time is called acceleration.Average acceleration is the change in velocity, v, divided by the time interval, t.

Acceleration occurs when an object speeds up, slows down, or changes direction. Average Acceleration:

The unit of acceleration is meters per second, squared: ms2Acceleration 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.

Use the image below to:Calculate the average velocity of the car.

Create a velocity vs time graph for the car.

Calculate the avg. acceleration of the car.

Develop an equation representing the relationship between the data.

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

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

The value of average acceleration varies with time intervals.Instantaneous acceleration is the slope of the tangent to the velocity vs. time graph at a given time.It can also be described as the limit of the average acceleration as the time interval goes to zero.

Chapter 2: One-Dimensional KinematicsSection 3: The Kinematic Equations

Velocity with Constant Acceleration:

Note that:This equation does not require displacement.vf v represents the velocity at any arbitrary time.V0 represents the initial velocity at t = 0. v = v0 + atDisplacement with Constant Acceleration:

Note that:This equation does not require acceleration.x = (v0 + v)t Displacement with Constant Acceleration:

Note that:t is actually t. However, ti is usually 0.The equation can be rewritten to find xi. x = v0t + at2 Velocity with Constant Acceleration:

Note that:This equation does not require time.x = (xf xi) v2 = v02 + 2axAll objects free fall with an acceleration of g = -9.8 m/s2.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.