Physics 20 – Graphing Uniform Accelerated Motion Motion where there is a constant change in speed is called uniform accelerated motion Acceleration Delta notation – A change in any quantity is indicated with the greek letter delta written as Δ. A change in time would therefore be written as Δt. Acceleration is defined as a change in velocity over time. Over time means that time is passing and in mathematics we sometimes see the word over as meaning division as it does here. Velocity is a vector and so will be acceleration. Acceleration can be determined using the equation  change in velocity
a=
time

 Δv
a=
Δt
The units for acceleration are a speed unit divided by a time unit (rate of change of m / s km / h
2
speed over time). These may look like , , km / h but the most common s
s
2
form is m / s . When answering questions it is important to know the definition of acceleration because it will allow you to determine if the situation requires you to consider as a uniform motion or uniform accelerated question. i.e. A car travelling at 30.0 m/s accelerates to 50.0 m/s in 20.0s. What is the acceleration of the car? 
 Δv
a=
Δt
v f − vi
a=
t
m
m⎞
⎛
⎜⎝ 50.0 − 30.0 ⎟⎠
s
s
a=
20.0s
m
a = 1.00 2
s
Graphical Analysis Uniform accelerated motion produces the following displacement-­‐time and velocity-­‐
time graphs. Displacement-­‐time Velocity-­‐time Notice that the slope of the distance-­‐time graph increases as time passes. This makes sense because the slope represents the speed on this graph and the speed is changing in accelerated motion. The velocity-­‐time graph shows that the velocity is increasing at a constant rate. In this case the slope will represent the acceleration. 
rise Δv 
slope =
=
= a run Δt