Position vs. time graphs
Review (x vs. t)
• Remember that for a position vs time graph that linear
lines show that object is moving at a constant velocity.
• The slope of the line at any point shows the
instantaneous velocity of the object.
Position vs. time graphs
(x vs. t)
• But what about curved lines like the one below?
Position vs. time graphs
(x vs. t)
• A parabolic curve means that the slope (velocity) is not
constant, so the object is accelerating. The object is
either speeding up or slowing down.
Definition of Acceleration
 An acceleration is the change in velocity
per unit of time. (A vector quantity.)
 A change in velocity requires the
application of a push or pull (force).
A formal treatment of force and acceleration will
be given later. For now, you should know that:
• The direction of acceleration is same as
direction of force.
• The acceleration is
proportional to the
magnitude of the force.
Average and Instantaneous a
aavg
Dv v2  v1


Dt t2  t1
ainst
Dv

(Dt  0)
Dt
slope
v2
Dv
Dv
v1
Dt
Dt
t1
t2
time
Speed Up or Slow Down?
If the velocity and acceleration both
positive, the object speeds up.
If the velocity and acceleration is both negative,
the object speed up.
If velocity and acceleration are opposite
signs, the object slows down.
Sames help each other (speed up) Opposites
hurt each other (slow down).
Velocity vs. time graphs
(v vs. t)
• Shows the change in velocity for an object over a period
of time.
• The slope of the line at any point shows the
instantaneous acceleration of the object.
• What is the acceleration
of this object from t=4 to
t=8 seconds?
5 m/s2
Velocity vs. time graphs
(v vs. t)
• The total area under the line tells you the change in
displacement (change in position) for the object in
motion.
• What is the change of displacement of the object from
t=0s to t=8s?
160 m
Velocity vs. time graphs
(v vs. t)
• Areas can be negative as well. In the case draw the line
to the zero x axis.
• What is the change of displacement of the object from
t=14s to t=20s?
-8 m
CONCLUSION OF Velocity
Time Graphs