Constant Acceleration
kinematic equations
Skytrain revisited
Skytrain Velocity
30
v (m/s)
20
acceleration
Constant acceleration
approximation
a = Δv
Δt
10
0 10 20 30 40 50 60 70 80 90 100 110 120 130
t (s)
Skytrain revisited
Skytrain Velocity
30
v (m/s)
20
10
acceleration
a = Δv
Δt
Positive
a
Negative
a
0 10 20 30 40 50 60 70 80 90 100 110 120 130
t (s)
Skytrain revisited
Skytrain Velocity
30
v (m/s)
20
10
acceleration
a = Δv
Δt
a= 0.35 (m/s)/s
0 10 20 30 40 50 60 70 80 90 100 110 120 130
t (s)
Skytrain revisited
Skytrain Velocity
30
v (m/s)
20
10
acceleration
a = Δv
Δt
2
a= 0.35 m/s
0 10 20 30 40 50 60 70 80 90 100 110 120 130
t (s)
Going the Other Way
When is a positive, when is a negative?
–10
–20
–30
Ne
g
at
ive
a = Δv
Δt
iti
ve
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Po
s
v (m/s)
t (s)
vf = vi + at
The
Kinematic
Equations
vf
∆x= vit + 1/2(vf–vi)t
a = Δv
Δt
v
∆x= 1/2vit + 1/2vft
1/ (v –v )t
2 f i
vi+vf
∆x= ————
2
vi
vit
ti
t
tf
t
vf = vi + at
vf
vavg
vi+vf
∆x= ————
2
vi
ti
t
tf
vavg=
vi+vf
t
————
2
vf = vi + at
vi+vf
∆x= ————
2
vf
a = Δv
Δt
vavg
t
∆x = vit + 1/2(vf–vi)t
vf–vi = at
vi
∆x = vit + 1/2(at)t
∆x = vit +
ti
t
tf
1/ at2
2
or
2
1
x = xi + vit + /2at
vf = vi + at
1/ at2
2
∆x = vit +
vi+vf
∆x= ————
2
vf
a = Δv
Δt
vavg
t
2
t= ————∆x
vf–vi = at
vi
vi+vf
vf–vi = at
2
vf–vi = a————∆x
v +v
i f
ti
t
tf
(vf–vi)(vf+vi)= 2a∆x
v2f –v2i = 2a∆x
vf = vi + at
1/ at2
2
∆x = vit +
vi+vf
∆x= ————
2
vf
v2f – v2i = 2a∆x
a = Δv
Δt
vavg
t
This is your arsenal of
weapons for kinematics
problems
vi
They work for constant
acceleration only.
ti
t
tf
You only need to
remember the basic
definitions — use algebra
to go from one to another.
and ALWAYS
draw a graphical representation of the
motion before using the equations.