June 6 -10, 2005

Solving Remedial Challenges KTeam and SCANS Institute The Little Red School House Approach:

Measuring Acceleration Due to Gravity

Three basic linear (straight-line) equations of the form y = mx + b, having variables of distance, time, velocity and acceleration, are the following: v f = v o + at v f 2 = v o ad d = v o t + ½ at 2 where v o is initial velocity, v f is final velocity, d is distance, a is acceleration, and t is time.

Three basic linear (straight-line) equations… v f = v o + at v f 2 = v o ad d = v o t + ½ at 2 Given any three of the five variables, the other two can be determined when v o is zero.

Three basic linear (straight-line) equations… v f = v o + at v f 2 = v o ad d = v o t + ½ at 2 These equations can be used to demonstrate that an object, falling freely under the influence of earth’s gravity, undergoes constant acceleration.

1/ v f = v o + at 2/ v f 2 = v o ad 3/ d = v o t + ½ at 2 When an object is dropped from a distance, or height h, acceleration “a” becomes “g” for gravitational acceleration during time t. If initial velocity is zero, Equation 3 becomes h = ½ gt 2

3/ d = v o t + ½ at 2 h = ½ gt 2 Using y = mx + b and graphing h versus t 2 give a straight line with slope equal to ½ g, so g equals 2 x slope

Time (sec) Time Squared Distance (cm)

h = ½ g t^2 Slope = ½ g g = 2 x slope

Dropped Ball “Measured” Data "Measured" DistanceTimeTime^2Calculated Distance (m)

“Measured” Video Frame Data

“Measured” d vs Time Squared Slope =LINEST(D3:D11, F3:F11) = 4.84 Slope = 1/2 g g = 2 x 4.84 = 9.68 Correlation Cofficient = CORREL(D3:D11, F3:F11) =

Dropped Ball “Measured” Data "Measured" DistanceTimeTime^2Calculated Distance (m)

“Measured” d vs Time