PASCO ME-9215B Photogate Timer - Manual (Page 12)

8
Photogate Timer 012-06379B
®
e
If the graph doesn't turn out to be a straight line (as it shouldn't), manipulate the data math-
ematically and replot it until you obtain a straight line graph. For example, try plotting dis-
tance as a function of
v
, v
2
, 1/v, etc. From your graph, what is the mathematical relation-
ship between the velocity of an object on an inclined plane and the distance from its starting
point that it has travelled along the plane?
Questions
c
The standard equations for motion with a constant acceleration (starting from rest) include:
x = 1/2 at
2 and v = at. Eliminate t from these equations to determine the relationship between
x and v. Using your result and your graph, can you determine the acceleration of the ball as it
rolled down the plane?
d
From your answer to question 1, write the equation of motion for the accelerating ball, giving
its position as a function time. Why do you think equations of motion are most often ex-
pressed as a function of time instead of simply relating position to velocity and acceleration?
Distance inside photogate =
ΔΔΔΔΔd:
Distance
Travelled
t
1
t
2
t
3
Final
Velocity
Average
Time
t
4
Table 2.1 Data and Calculations