LAB3.4: 1-D Kinematics - Constant Acceleration Relationships
Name: _________________________________Class Period: ______ Date: __________
PURPOSE
The purposes of this activity are to illustrate and compare various aspects of graphical
and algebraic analysis for an object undergoing constant acceleration.
BACKGROUND
In this unit, we have learned a number of concepts regarding the relationships between
position, velocity, and acceleration:
1. The instantaneous velocity is equal to the ______________ of the
____________-____________ graph
2. The instantaneous acceleration is equal to the _______________ of the
____________-____________ graph
3. The change in position between two times is equal to the corresponding
__________________ the ____________-____________ graph
4. The change in velocity between two times is equal to the corresponding
__________________ the ____________-____________ graph
We are also aware that the average velocity and the average acceleration between two
times are given by the equations:
v
x2  x1
t 2  t1
a
v2  v1
t 2  t1
In addition, we have examined constant acceleration scenarios and realized that:
1. the shapes of the graphs for the kinematic variables are polynomial functions:
a. position-time: ____________________
b. velocity-time: ____________________
c. acceleration-time: _________________
2. the corresponding equations that relate the kinematic variables under constant
acceleration conditions are as follows:
PROCEDURE
The experimental apparatus used to collect data for this activity is illustrated below. The
cart was released from rest at a distance of approximately 40.0 cm from the motion
sensor. Data (see the graphs below) was collected for a time period of 0.80 seconds, as
the cart sped toward the right.
MOTION
SENSOR
CART
STRING
MASS
DATA
Time (sec)
Time(sec)
Time(sec)
ANALYSIS
Step#1: Identifying the overall shapes of the graphs
Identify the polynomial functions that best describe the shapes of the three graphs:
a. position-time: ____________________
b. velocity-time: ____________________
c. acceleration-time: _________________
Step#2: Quantities that can be determined from the Position-Time Graph
Time (sec)
a. Initial Position (xi) and Final Position (xf) [read directly from the position-time
graph]
b. Initial Velocity (vi) [slope of a line that is tangent to the position-time graph at
t=0.00 sec]
c. Final Velocity (vf) [slope of a line that is tangent to the position-time graph at
t=0.80 sec]
d. Average Velocity ( ) [total change in position divided by the change in time]
Step#3: Quantities that can be determined from the Velocity-Time Graph
Time (sec)
a. Total Change in Position (d = xf - xi) [total area under the velocity-time graph]
b. Average Velocity ( ) [total area under the velocity-time graph divided by the time
interval]
c. Initial Velocity (vi) and Final Velocity (vf) [read directly from the velocity-time
graph]
d. Average Acceleration ( ) [total change in velocity divided by the change in time]
e. Acceleration (a) [can be approximated as the slope of the velocity-time graph at
any time, in this case it is equal to the average acceleration because the velocitytime graph is linear]
Step#4: Quantities that can be determined from the Acceleration-Time Graph
(use the dashed line approximation to the actual data)
Time (sec)
a. Total Change in Velocity(Δv = vf - vi) [total area under the acceleration-time
graph]
b. Average Acceleration ( ) [determined from the acceleration-time graph by visual
approximation … can also be found by dividing the total area under the
acceleration-time graph by the time interval]
c. Acceleration (a) [determined from the acceleration-time graph by visual
approximation]
Step#5: Introduction to the mathematical equations for constant acceleration
a. Record your best estimates of the following quantities from the first four steps:
xi = ____________
vi = ____________
a = ____________
t = _____________
b. Find the final position using:
c. Find the final velocity using:
d. Find the final velocity using:
CLOSING REMARKS: You should have found that the different methods for
determining the same quantity lead to very similar results. This activity is a great
resource for reviewing what can be determined from each type of graph.