Velocity-Time Graphs
You’ll be doing the same 3 things with these graphs...
·
-
Reading the values
-
Finding the slope gives us the acceleration of the object, not the direction that
the object is moving in.
-
The direction an object is moving in can be determined from the quadrant it is
graphed in......
If in quadrant 1, movement is up, north, right, or east.
If in quadrant 4, movement is down, south, left, or west.
-
Calculating the area between the line and the x-axis of the graph....only this time
it means something...your answer will be the displacement of the moving
object !
The velocity vs. time graph (in future referred to as a v-t graph) for uniform motion
is a horizontal line.
v
v
t
Since motion is in quadrant 1
object is moving E(right) or
N(up).
·
Since motion is in quadrant 4
object is moving W(left) or
S(down).
t
The velocity vs. time graph for uniform acceleration* is a diagonal line.
uniform acceleration means the velocity of a moving object is changing by the
same amount for each time interval.
Speeding up and moving
left, down , S or W
v
v
t
t
Speeding up and moving
right, up, N or E
Object is slowing down
and moving left, down,
south, west.
v
v
t
t
Slowing down and
moving right, up, N or E
NOTE:
In math the bigger the negative number the smaller the number ( -40 < -10). However, in
physics negative signs indicate direction... not the size of a number.
-40km/h is greater than -10km/h because -40 km/h means 40 km/h [W, S, L, D]
and -10 km/h means 10 km/h [W, S, L, D]. Common sense tells us 40 > 10.
-
Instantaneous velocities can be read directly from the graph.
The y-intercept of a v-t graph for uniform acceleration represents the
initial velocity.
-
The slope of the line gives acceleration of the object.
-
The area between the line and the time axis gives us the displacement for that
time interval.
Example 1....
A)
Determine the displacement of the object during the 10 second trip
graphed below.
B)
Find the acceleration of the object over the first four seconds. (Slope)
C)
Describe the motion of the object during
i. During the first four seconds
ii. During the last six seconds
Example 2....
A)
B)
Determine the displacement of the object during the 20 second trip
graphed below. (Assume that the little curves don’t exist)
Find the acceleration of the object between five and ten seconds. (Slope)
C)
Find the acceleration of the object between fifteen and twenty
seconds. (Slope)
D)
Describe the motion of the object during the twenty second trip
Practice questions :
Page 456, #’s 1, 2
Page 472, #’s 4, 11 (also find the acceleration (slope))