Lab 2: Graphs of Position, Velocity and Acceleration
Name: __________________________
Goals:
- Learn to graph and interpret graphs of position, velocity and acceleration as functions of time.
- Understand the directions of velocity and acceleration vectors for objects moving with constant acceleration.
Position, Velocity and Acceleration as functions of time:
In one-dimensional kinematics, we can describe the position, velocity or acceleration of an object as a function of time by using a
two-dimensional graph. We put time on the horizontal axis and position, velocity or acceleration on the vertical axis. By convention,
positive values of position, velocity or acceleration mean “rightward” or “upward” depending on the context, while negative values
mean “leftward” or “downward”.
There are several important relationships between position, velocity and acceleration graphs:
Type of Graph
Position vs. Time, x(t )
Velocity vs. Time, v(t )
Meaning of Slope
Velocity
Meaning of Signed Area
Acceleration
Displacement (change in position): x
Change in velocity: v .
Acceleration vs. Time, a(t )
Attaching velocity and acceleration vectors to an object:
When we are visualizing a kinematics problem, it is often useful to draw velocity and acceleration vectors on the object. For
example, if I tell you that a car is moving to the right and speeding up, the picture would look like this:
v
a
Since the acceleration is positive, the change in velocity is positive over the next second, so the car moves faster to the right.
However, if a car is moving to the right but slowing down, the picture would look like this:
a
v
The negative acceleration makes the velocity change by a negative amount over the next second – so the positive velocity is reduced
(the car moves slower).
Each of the following graphs represents the motion of a car travelling on a dynamics track. Use the given graph to fill in the other
graphs, then provide the requested vector diagram. For each picture, check your work by moving your dynamics cart along the track
by hand. Each lab group should print the graphs of x(t ), v(t ) and a(t ) for each part of the lab. You can get all three graphs on a
single page in Logger Pro for each part.
1.
x
v
t
a
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion described in the graphs:
2.
x
v
t
a
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion described in the graphs:
3.
x
v
t
a
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion described in the graphs:
4.
x
v
a
t
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion during the first half of the trip:
Draw qualitative velocity and acceleration vectors on the cart for the second half of the trip:
5.
x
v
a
t
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion during the first two time units:
Draw qualitative velocity and acceleration vectors on the cart for the motion during the last two time units:
6.
x
v
a
t
t
t
Draw qualitative velocity and acceleration vectors on the cart for the motion during the first two time units:
Draw qualitative velocity and acceleration vectors on the cart for the motion during the last two time units:
7. Sketch the graphs of x(t ), v(t ) and a(t ) for the bean bags in the free-fall experiment at the end of Lab 1.
x
v
t
a
t
t