Chapter 2

Chapter 2Kinematics in One DimensionAnalyzing MotionDisplacementThe displacement of an object is a vector that points from an object initial position to its final position and has a magnitude that equals the shortest distance between the two positions. SI Unit: meter (m)When motion is along a straight line, directions can be assigned as positive or negative

More Displacement

The displacement is the difference between the final and initial position of an object. Remember that delta means change in. The change in any variable is always the final value minus the initial value.

Speed and VelocitySpeed can be described as how fast an object is moving.Average speed is the distance traveled divided by the time required to cover the distance.SI unit: m/s

Speed DOES NOT tell you anything about direction.Average VelocityAverage velocity is found by dividing the displacement by the elapsed time. SI unit: m/sAverage velocity is a vector that points in the same direction as the displacement. Again, for one dimension, + or can be used to indicate direction of velocity.

Instantaneous VelocityThe instantaneous velocity of an object indicates how fast the object moves and the direction of the motion at each instant of time.

Questions So FarWhat is the difference between speed and velocity?Give an example of positive velocity and negative velocity.Explain how average velocity and instantaneous velocity are different.http://he-cda.wiley.com/WileyCDA/HigherEdMultiTitle.rdr?name=cutnellDisplacement vs. Time GraphsThe slope of a displacement vs. time graph will tell you the velocity of the object.If the slope is positive, the velocity is positive.It should go without saying that if the slope is negative, the velocity is negativeLook at a Few Examples

Constant VelocityPositive Velocity

Positive VelocityChanging Velocity (acceleration)

Fast, Leftward(-)Constant Velocity

Negative (-) VelocitySlow to Fast

Leftward (-) VelocityFast to SlowHow could we find the instantaneous velocity in any of these situations?Velocity vs. Time GraphsThe slope of a velocity vs. time graph reveals useful information about the acceleration of an objectIf the acceleration is zero, the slope is zero (horizontal)If acceleration is positive, slope is positiveIf the acceleration is negative, slope is negativeReading Velocity vs. Time Graphs

http://www.physicsclassroom.com/Class/1DKin/u1l4c.cfm

The Area Under the Curve of a V-t graphThe area under the curve of a velocity vs. time graph can be used to determine the displacement of an object.

AccelerationAcceleration comes into discussions of motion when the change in the velocity is combined with the time during which the change occurs.Average Acceleration is a vector that points in the same direction as As with velocity, plus and minus signs indicate the two possible direction for the acceleration vector when motion is along a straight line.

Definition of Average Acceleration

Instantaneous acceleration is a limiting case of the average acceleration. When the time interval for measuring the acceleration becomes extremely small, the average acceleration and the instantaneous acceleration become equal. In most situation we deal with acceleration is constant or uniform.SI unit of acceleration: m/s2Sample ProblemA drag racer crosses the finish line, and the driver deploys a parachute and applies the brakes to slow down. The driver begins slowing down when t = 9.0s and the cars velocity is +28m/s. When t = 12.0s, the velocity has been reduced to +13m/s. What is the average acceleration of the dragster?Negative and Positive AccelerationWhenever the acceleration and velocity vectors have opposite directions, the object slows down and is said to be decelerating.When the acceleration and velocity vectors point in the same direction, the object speeds up and has positive (+) acceleration.

Equations of Kinematics for Constant AccelerationWe have now discussed the motion of objects along a straight line in terms of the following quantitiesDisplacementVelocityTimeAccelerationThe kinematics equations use no new concepts but relate these terms in easy to use equations.These equations need only be derived one time, then used over and over.Derivation AssumptionsObject is located at the originwhen . Then, x becomes x.Dispense using boldface symbols and small arrows for displacement, velocity, and acceleration vectors.Continue to use + or for direction. Essentially, kinematics equations rearrange and recombine existing equations in order to make problem solving easier.

Kinematics Equations1. Start with acceleration equation and rearrange to solve for v.

2. Using the average velocity formula and assuming x0 and t0 to be zero, x = vt .Since the velocity increases at a constant rate, the average velocity is midway between v0 and v.

Kinematics Equations Continued3. Combining equations one and two into a single equation by algebraically eliminating the final velocity (v) expression for displacement (x) will result.

4. Finally, by combining the average acceleration formula (rearranged to solve for t) and equation number 2, an expression of motion not involving time can be derived.

Hints for Solving So FarDraw a PictureDecide which direction will be positive (+) and which will be negative (-)While you are reasoning the problem, be sure to interpret the terms decelerating or deceleration correctlyIf the motion of two objects are interrelated, data for only two variable need to be specified for each object.If motion is divided into segments, with different acceleration, realize that final velocity for one is initial velocity for the other.Freely Falling BodiesIn general, all bodies at the same location above the earth fall vertically with the same acceleration.When we neglect air resistance and consider acceleration nearly constant, we are considering free fall and can use kinematics equations in problem solvingg = 9.8m/s2Using Kinematics Equations for Free Fallg on the moon is approx 1/6 that of g on EarthOften, the symbol y is used for vertical displacementWhen an object is dropped, v0 = 0m/sThe acceleration due to gravity is ALWAYS a downward-pointing vector.Free Fall Up?Free Fall refers to any object moving either upward or downward under the influence of gravity aloneIn either case, the object always experiences the same downward acceleration due to gravity