Motion Graphs 2
x
v
a
Slope in Kinematics
Velocity is the rate of change of position, i.e.
how fast position changes over time.
d
v
t
or
x rise
v

 slope of x(t ) graph
t run
Acceleration is the rate of change of velocity,
i.e. how fast velocity changes over time.
v
a
t
or
v rise
a

 slope of v(t ) graph
t run
Motion Graphs for a Car
Speeding up from Rest
v(m/s)
x(m)
Slope of x(t)
0
2
4
6
t(s)
1 2
x  at  3t 2 (upward parabola )
2
0
1
3
5
t(s)
v f  at  6t ( slope )
For a car that starts at rest (vi=0) and speeds up
at a rate of a=6 m/s2.
Motion Graphs for a Car
Slowing Down to Rest
v(m/s)
x(m)
Slope of x(t)
0
2
4
6
t(s)
0
1
3
5
t(s)
1 2
x v i t  at  3t 2  5t [downward parabola ] v f  at  6t  5 [ slope ]
2
For a car that is pushed with a certain velocity (vi>0)
and slows down to rest at a rate of a=-6 m/s2.
Motion Graphs for a Car
Speeding up from Rest
v(m/s)
a(m/s2)
Slope of v(t)
0
1
3
5
t(s)
v f  at  6t [ slope ]
0
1
3
5
t(s)
a  6 [ constant ]
For a car that starts at rest (vi=0) and speeds up
at a rate of a=6 m/s2.
Motion Graphs for a Car
Speeding up from Rest
v(m/s)
a(m/s2)
Slope of v(t)
0
1
3
5
t(s)
0
1
3
5
t(s)
v f  at  6t  5 [ slope ]
a  6 [ constant ]
For a car that is pushed with a certain velocity (vi>0)
and slows down to rest at a rate of a=-6 m/s2.
Slope in Accelerated Motion
x(m)
v(m/s)
a(m/s2)
Slope of v(t)
Slope of x(t)
0
2
4
x
6
t(s)
0
slope
1
3
v
5
t(s)
0
slope
1
3
a
5
t(s)
Slope in Decelerated Motion
x(m)
v(m/s)
a(m/s2)
Slope of x(t)
0
2
4
6
x
t(s)
Slope of v(t)
0
slope
1
3
v
5
t(s)
slope
t(s)
0 1
3
a
5