1. The Equations of Motion
Kinematics
The Equations of Motion

2. Equations of Motion
The equations of motion all apply to a body moving…
…with constant acceleration
…in a straight line.
They can also be applied to projectile motion.

3. 1. The average velocity equation:
We know that if an object accelerates uniformly from an initial velocity (u) to a final velocity (v) over a time (t) then…
If it has travelled through a displacement (s) then also…
So…
Or…
Average velocity = u + v
Average velocity = s t
s = u + v t a
s = ½ (u + v) t

4. 2. The acceleration equation
We know that acceleration is given by…
Rearranging gives…
Acceleration = v - u t
v = u + at b

5. 3. The displacement equation
Substituting b into a gives…
So…
s = ½ (u + u + at) t
s = ½ (2u + at) t c
s = ut + ½ at2

6. The fourth equation t = 2s (u+v) (v–u) (u+v) = 2as v = u + a 2s (u+v)
Rearranging a gives…
Substituting into b gives…
Rearranging…
So…
Expand the brackets…
Simplifies to…
t = s (u+v)
(v–u) (u+v) = 2as
v = u + a 2s
(u+v)
uv + v2 – u2 – uv = 2as
v-u = 2as
(u+v)
v2 = u2 + 2as d

7. Note:
When recalling the equations of motion, check for homogeneity if you’re not sure.
e.g.
s = ut + ½ at2

8. Question
First watch this video.
Now, analyse the video to determine…
- fall time
- height of cliff
- velocity upon impact

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