1. Motion in one dimension
Chapter 2
Motion in one dimension

2. One-Dimensional Motion with Constant Acceleration
Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity.
The final velocity equals the initial velocity plus the acceleration x time
vx = v0 + at
v2x = v2x0 + 2ax(Δx)
The final position equals the initial position plus the velocity multiplied by time plus one hals the acceleration multiplied by the time squared
x = x0 + vx0(t) + ½ at2

3. One-Dimensional Motion with Constant Acceleration

4. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
Initial velocity
Changing velocity
Acceleration (constant)
Positive velocity
Positive acceleration

5. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
Initial velocity
Constant velocity, positive
Acceleration, constant, zero

6. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
Initial velocity
Changing velocity
Acceleration (negative), constant

7. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
Changing velocity
Initial velocity
Acceleration, negative
Acceleration is not constant, decreasing acc. over time

8. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
Changing velocity
Acceleration, positve
Acceleration not constant

9. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
No initial velocity, accelerates at a constant rate during the A period
No acceleration, constant velocity during the B period
Negative acceleration during the C period
At the end of the observation, the object is still moving

10. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
a = +1 m/s2

11. Velocity vs. Time Graph
The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information.
a = +0.3 m/s2
a = +3 m/s2
a1 = +1.6 m/s2
a2 = -1.6 m/s2

12. Velocity vs. Time Graph
The slopes of one graph can be graphed as well and so on…

13. Freely falling objects
We usually disregard air resistance.
A “freely falling object is moving under the influence of gravity alone.
e.g. cannonball, arrow, something dropped, planetary motion, etc…
Free-fall acceleration on Earth, g, m/s2
Typical problems include:
The impact speed of an object dropped from a known height
Calculating the height of a fall

14. Freely falling objects
To find the displacement of an object thrown straight up, y = y0 + v0t + ½ at2
You may need to calculate time to the highpoint first
Keep in mind that, at the highpoint, vy = 0
vy = voy + at

15. Freely falling objects