Interpreting position, velocity, speed ,
and acceleration graphs
• Anytime you are given a position or velocity graph
and you need to find information about the position,
velocity, speed, and acceleration sketch a graph of
the following.
– S(t) is the position function
– V(t) is the velocity function
– A(t) is the acceleration function
Describing Motion
Looking at the velocity graph
Looking at the position graph
Forward
V(t)>0
Slopes of s(t) are positive
Look at the Velocity Graph and
see when it is above the x-axis
Look at the position graph and
see when it is increasing
V(t)<0
Slopes of s(t) are negative
Look at the Velocity Graph and
see when it is below the x-axis
Look at the position graph and
see when it is decreasing
V(t) = 0
Slopes of s(t) are zero
Look at the Velocity Graph and
see when it is on the x-axis
Look at the position graph and
see when it is constant
V(t) = 0
s(t) is a maximum or a minimum
Look at the velocity graph and
see when it changes from above
to below or from below to
above
Look at the position graph and
see when it changes from
increasing to decreasing or from
decreasing to increasing
Backward
Standing still
Changing Direction
Describing Speed
Look at Speed Graph
Look at Velocity Graph
Speed up
Speed Graph is going up
V(t) increasing
Look at the Velocity Graph and
see when it is going away from
the x-axis (moving up/above the
x-axis)
This should happen after the
velocity = 0 (after you change
directions or at the beginning)
Speed graph is increasing
V(t) is decreasing.
Look at the velocity graph and
see when it is going away from
the x-axis (moving down/below
the x-axis)
This should happen after the
velocity = 0 (after it changes
directions or at the beginning .
Describing Speed
Look at Speed Graph
Look at Velocity Graph
Slow Down
Speed graph is going down
V(t) increasing
Look at the Velocity Graph and
see when it is going toward the
x-axis (moving up from below
the x-axis)
This should happen as the
velocity is getting close to 0 (as
you are getting ready to change
directions/getting ready to
cross the x-axis)
Speed graph is decreasing
V(t) is decreasing.
Look at the velocity graph and
see when it is going toward the
x-axis(moving down from above
the x-axis)
This should happen as the
velocity is getting close to 0 (as
you are getting ready to change
directions/getting ready to
cross the x-axis)
Describing Speed
Look at Acceleration
Graph
Look at Velocity Graph
Look at Speed Graph
Change Speeds
Acceleration = 0
Velocity = 0
Changes direction
Describing acceleration
Looking at the acceleration graph
Looking at the velocity
graph
Acceleration positive
a(t) > 0
v(t) increasing
Look at the acceleration graph and
see when it is above the x-axis
Look at the Velocity Graph
and see when it is going up
a(t) > 0
v(t) decreasing
Look at the acceleration graph and
see when it is below the x-axis
Look at the Velocity Graph
and see when it is going
down
a(t) = 0
v(t) constant
Look at the acceleration graph and
see when it is on the x-axis
Look at the Velocity Graph
and see when it is constant
Acceleration negative
Acceleration equals 0