Motion in One Dimension

Movement along a straight-line path  Linear motion Convenient to specify motion along the x and y coordinate system

Motion in One Dimension Important to specify magnitude & direction of motion (Up or down; North, South, East, or West) Coordinate (x and y) axes Objects right of origin on x axis = positive Objects left of origin on x axis = negative Objects above origin on y axis = positive Objects below origin on y axis = negative POSITION: Location of an object relative to an origin

Displacement versus Distance Displacement (x) Distance & direction Measures net change in position Displacement may not equal total distance traveled

Distance Distance Total path length traversed in moving from one location to another Example: Jimmy is driving to school but he forgets to pick up Johnny on the way…He now has to reverse his direction and drive back 2 miles Total Distance Traveled = 12 miles Total Displacement = 8 miles + 10 miles - 2 miles

Vector Quantity with both magnitude and direction * Represented by arrows in diagrams

Displacement

Velocity Average velocity Average velocity is the displacement divided by the elapsed time.

Speed versus Velocity Speed: Positive number, with units Does not take into account direction Speed is therefore a _ _ _ _ _ _ quantity? Velocity (v): Specifies both the magnitude (numerical value  how fast an object is moving) and also the direction in which an object is moving Velocity is therefore a _ _ _ _ _ _ quantity?

Average Velocity The football player ran 50 m in 20 s. What is his average velocity? v = 50 m / 20 s = 2.5 m/s

Velocity The World’s Fastest Jet-Engine Car Andy Green in the car ThrustSSC set a world record of m/s (762.8 mph) in To establish such a record, the driver makes two runs through the course, one in each direction, to nullify wind effects. From the data, determine the average velocity for each run.

Velocity (759 mph) (766.4 mph)

Acceleration Acceleration (a) Change in velocity per time interval Animation of constant acceleration website

Acceleration Acceleration and Decreasing Velocity

Acceleration

Acceleration Acceleration: Vector quantity  Positive acceleration –  Velocity increasing Negative acceleration –  Velocity decreasing SI units for acceleration: meters/second 2  m/s 2 Acceleration Animation Website Animation - Direction of Acceleration and Velocity Website

Motion Equations for Constant Acceleration Constant Acceleration: Instantaneous & average accelerations are equal

1. Displacement  x (meters) 2. Acceleration (constant)  a (m/s 2 ) 3. Final velocity  v (m/s) 4. Initial velocity  v o (m/s) 5. Elapsed time  t (s) Variables

Motion Equations for Constant Acceleration

Solving Problems Draw a depiction of the situation Utilize x and y coordinate axes with +/- directions Write down known variables Select appropriate equation Complete calculation **UNITS! Reasonable result?

Example: Catapulting a Jet ** Find its displacement.

An Accelerating Spacecraft A spacecraft is traveling with a velocity of m/s. Suddenly the retrorockets are fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s 2. What is the velocity of the spacecraft when the displacement of the craft is +215 km, relative to the point where the retrorockets began firing? xavvovo t m-10.0 m/s 2 ?+3250 m/s

xavvovo t m m/s 2 ?+3250 m/s v = 2503 m/s

Falling Objects  Galileo Galilei’s  Galileo Galilei’s Contribution  In the absence of air resistance, all objects on Earth fall with the same constant acceleration.  Acceleration due to gravity (g) = 9.8m/s 2

Free-fall Any freely falling object being acted upon solely by the force of gravity Ignore air resistance Rate of acceleration due Earth’s gravity g = 9.8 m/s 2 Vector  Direction is towards the center of the Earth

Free Fall  Object does not have to be falling to be in free fall  Example - Throwing a ball upward  Motion is still considered to be free fall, since it is moving under the influence of gravity

Constant Acceleration Equations Acceleration due to Gravity Equations Acceleration due to Gravity Equations

A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement y of the stone?

yavvovo t ? m/s 2 0 m/s3.00 s

yavvovo t ? m/s 2 0 m/s3.00 s

How High Does it Go? The referee tosses the coin up with an initial speed of 5.00m/s. In the absence of air resistance, how high does the coin go above its point of release?

yavvovo t ? m/s 2 0 m/s m/s

yavvovo t ?-9.80 m/s 2 0 m/s+5.00 m/s