1D Motion, Constant Acceleration

"Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occured to him to verify this statement by examining his wives' mouths"
Bertrand Russell

Speed - Rate at which distance is covered

Average speed = (Total distance travelled)/(Total time taken)

how

Instantaneous speed = slope of distance versus time graph evaluated at a particular point

Units of speed - m/s (SI) or ft/s (British)

Velocity - Vector quantity, speed in a specific direction

Acceleration - Rate of change of speed (velocity) with time

Average acceleration = (Final velocity - Initial velocity)/(Total time)
Instantaneous acceleration = slope of speed versus time graph at a particular point

Acceleration can be positive or negative, negative acceleration is often called deceleration
Units of acceleration - m/s² (SI) or ft/s² (British)

Kinematic equations for one dimensional constant acceleration motion

v_f = v_i + at
x = v_i t + at² /2
x = (v_f ² - v_i² )/2a
x = (v_i + v_f )t/2

Vertical motion under the influence of gravity (ignoring air resistance).

Galileo determined that

"All freely falling objects have the same acceleration at the same place near the earth's surface"

The value of this acceleration is 9.8 m/s² (32 ft/s²) directed towards the centre of the earth.
Since the acceleration is constant, the kinematic equations above may be applied, where a=-g, the v's represent velocities in the y (vertical) direction and x becomes the distance in y (height).

It is said that in order to come to the above conclusion Galileo performed a number of experiments by dropping pairs of different objects off the Leaning Tower of Pisa. One such pair were reputed to be a feather and a stone. Of course the stone hits the ground first. However, in the vacuum of the Moon this is not the case, the stone and feather will hit the ground at the same time. Apollo 15 astonauts David Scott and Jim Irwin actually conducted this experiment on the Moon, the results of which are documented on NASA's Lunar Feather Drop Home Page.

"The search for the man who terrorizes nudist camps with a bacon slicer goes on. Inspector Lemuel Jones had a tip-off this morning, but hopes to be back on duty tomorrow."
Ronnie Barker

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu