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Motion in One Dimension. 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)

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motion in one dimension1
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 dimension2
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


    • Location of an object relative to an origin
displacement versus distance
Displacement versus Distance
  • Displacement (x)
    • Distance & direction
    • Measures net change in position
  • Displacement may not equal total distance traveled
  • 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

- 2 miles

+ 10 miles


Quantity with both magnitude and direction

* Represented by arrows in diagrams


Average velocityis the displacement divided by the elapsed time.

speed versus velocity
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
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


The World’s Fastest Jet-Engine Car

Andy Green in the car ThrustSSC set a world record of

341.1 m/s (762.8 mph) in 1997. 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.


(759 mph)

(766.4 mph)

  • Acceleration (a)
    • Change in velocity per time interval

Animation of constant acceleration website


Acceleration and Decreasing


  • Acceleration:
    • Vector quantity 
      • Positive acceleration
        •  Velocity increasing
      • Negative acceleration
        •  Velocity decreasing
  • SI units for acceleration:
    • meters/second2  m/s2

Acceleration Animation Website

Animation - Direction of Acceleration and Velocity Website

motion equations for constant acceleration
Motion Equations for Constant Acceleration
  • Constant Acceleration:
    • Instantaneous & average accelerations are equal

1. Displacement  x (meters)

2. Acceleration (constant) a (m/s2)

3. Final velocity  v (m/s)

4. Initial velocity  vo (m/s)

5. Elapsed time  t (s)


Motion Equations for

Constant Acceleration

solving problems
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 +3250 m/s. Suddenly the retrorockets are fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s2. What is the velocity of the spacecraft when the displacement of the craft is +215 km, relative to the point where the retrorockets began


falling objects
Falling Objects
  • 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/s2
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/s2
    • Vector 
      • Direction is towards the center of the Earth
free fall1
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

Acceleration due to Gravity Equations

Constant Acceleration



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?


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?