Distance vs. Time in Accelerated Motion

 

Graph by De'sirae based on data collected in class

According to the equation of accelerated motion, d₀ = at²/2 + v₀t + d₀,
the parameters of motion are:

• Acceleration a = 0.11 m/s²
• Original velocity v₀ = 0.24 m/s
• Original distance d₀ = 0.40 m

One more attempt to graph displacement vs time

Both graphs are done by Lenicha in Excel. Good job! 

Just one observation.  In the graph below, points are precisely placed on a parabola (trendline option of a second-degree polynomial).  That suggests a question about the graph above, which presents quite scattered points.  The only reasonable explanation is in the launching method; the launcher equipped with a rubber band might not be the best solution.  

Both graphs present a good start-point for further discussion in class. 

Accelerated motion

The time of glider passing between photogates is measured with high accuracy (0.001 s). 

The same video in low motion:

Distance in accelerated motion

The air track is elevated (see its right leg in the picture), so the observed motion is accelerated due to gravity. Two photogates allow to measure the time needed to move between them with high accuracy. In our experiment the second photogate was placed each time 10 cm farther to the left (see the data below). 

(Graph by Tim)

Speed in accelerated motion

The glider blocks the photogate passing through. If the glider's flag is 10 cm long and the measured time is 0.214, then the speed of the glider is

v = l / t

v = 0.1 m / 0.2157 s = 0.4636 m/s

Once again, now in slow motion:

Speed in accelerated motion

The photogate measures time of the glider passing through. To calculate its speed, use the length of glider's flag. Moving the photogate farther allows to measure the increasing glider's speed:

v = l / t

l = 10 cm = 0.1 m.

(Graph by Tim)

The graph shows that speed increases at the same rate.