1. Constant Acceleration

2. Graphs to Functions
A simple graph of constant velocity corresponds to a position graph that is a straight line.
The functional form of the position is
This is a straight line and only applies to straight lines. x t x0 v t v0

3. Constant Acceleration
Constant velocity gives a straight line position graph.
Constant acceleration gives a straight line velocity graph.
The functional form of the velocity is v t v0 a t a0

4. Top Fuel
A top fuel dragster can reach 150 m/s (330 mph) in 3.7 s. What is the acceleration?
In the equation v0 = 0
The acceleration is v/t.
a = 41. m/s2
Credit: Lt. Col. W. Thurmond, U.S. Army

5. Acceleration and Position
For constant acceleration the average acceleration equals the instantaneous acceleration.
Since the average of a line of constant slope is the midpoint: v t
a0(½t) + v0 ½t v0

6. Acceleration Relationships
Algebra can be used to eliminate time from the equation.
This gives a relation between acceleration, velocity and position.
For an initial or final velocity of zero. This becomes
x = v2 / 2a
v2 = 2 a x
from

7. Drag Strip
A top fuel dragster accelerates at 40. m/s2 for 3.7 s. How far does the car go on the track?
Starts at rest and at 0.
x = 270 m
Credit: Lt. Col. W. Thurmond, U.S. Army

8. Accelerating a Mass
A loaded 747 jet has a mass of 4.1 x 105 kg and four engines.
It takes a 1700 m runway at constant thrust (force) to reach a takeoff speed of 81 m/s (290 km/h).
What is the force per engine?
The distance and final velocity are used to get the acceleration.
The acceleration and mass give the force.