1. Kinematics
Motion Graphs

2. Consider units! Motion Graphs 1. Displacement – Time graphsb c d
a = uniform positive velocity
b =
c =
d =
a = uniform positive velocity
b = decreasing pos velocity
c = at rest
d = uniform negative velocity
Consider units!

3. The gradient of a displacement - time graph is equal to the velocity of the object at any instant.
gradient = Δy = Δ displacement = Δs = velocity
Δx Δ time Δt
Instantaneous velocity is given by the gradient of the tangent to the line at a certain time, t. Δy Δx
time
displacement t
v = m = Δy Δx

4. Consider units! 2. Velocity – Time graphsb c d
a = uniform positive acceleration
b = non uniform positive acceleration
c = uniform velocity
d = uniform negative acceleration (perhaps a deceleration)
a = uniform positive acceleration
b =
c =
d =
Consider units!

5. The gradient of a velocity - time graph is equal to the acceleration of the object at any instant.
gradient = Δy = Δ velocity = Δv = acceleration
Δx Δ time Δt
Instantaneous acceleration is given by the gradient of the tangent to the line at a certain time, t.
The area under any section of a v-t graph is equal to the total displacement over that time period. (So you could have a negative area, indicating negative displacement)
area = average velocity x time = v x Δt = Δs

6. Consider units! 3. Acceleration – Time graphs
We are mainly interested in uniform acceleration:
Acceleration
Time a b
a = uniform positive acceleration
b = uniform negative acceleration
Consider units!

7. Q.
Two masses follow the paths shown. By sketching a velocity time graph for each, determine which one will reach the end of the track first? v t A v t B
A. They both travel the same total distance, therefore the area under the v-t graph must be the same. Thus ball B must reach the end first!