1. Announcements No class next Monday (MLK day)
Do MasteringPhysics homework
Homework 00 open ‘til Friday 10 PM
Homework 01 will open soon
Written Homework due next Friday
Book problems 2.37 and 2.71

2. Describing Motion
acceleration
§2.3–2.4

3. Board Work
A car waits at a stop light for 5 seconds, smoothly accelerates to 15 m/s over 5 seconds, and then continues at 15 m/s. Describe the car’s motion using a velocity-time graph.

4. Acceleration Rate of changing velocity Dv average acceleration = Dt
over the entire interval Dv Dt
at one instant
instantaneous acceleration = lim
= dv/dt
= d2x/dt2

5. Poll Question What is the SI unit for acceleration? m. s. m·s. m/s.

6. Visualize Acceleration
Board Work:
Signs of v
Signs of a
Young and Freedman, Fig. 2.8

7. Group Work In earlier car scenario:
What is the car’s acceleration during the different segments of its motion?
Describe the car’s motion using an acceleration-time graph.

8. Equations of Motion
as functions of time

9. Find Position from Velocity
Generally: velocity is derivative of position wrt time dx/dt.
Conversely, position is the integral of velocity over time.
v = dx/dt
dx = v dt
∫dx = ∫v dt
x = ∫v dt + x0
What is this when v is constant?

10. Integral of v-t graph area = (a m/s)(b s) = ab m speed (m/s)
distance units
speed (m/s) a b
time (s)

11. Constant Acceleration
Instantaneous accel = average accel
a = Dv/Dt
Dv = velocity change over time Dt
Dv = a Dt
v = v0 + Dv = v0 + a Dt

12. Find Velocity from Acceleration
General case: acceleration is derivative of velocity wrt time dv/dt.
Conversely, velocity is the integral of acceleration over time.
a = dv/dt
dv = a dt
∫dv = ∫a dt
v = ∫a dt + v0
What is this when a is constant?

13. Equations of Motion
What are velocity and position under conditions of constant acceleration?

14. Formulas from Constant x-Acceleration
Velocity change Dv = a Dt
Velocity vt = v0 + Dv = v0 + a Dt
Position change Dx = v0 Dt + 1/2 a (Dt)2
Position xt = x0 + v0 Dt + 1/2 a (Dt)2

15. Another Form (constant a)
If you don’t know Dt and want v:
x = x0 + v0Dt + 1/2 a (Dt)2 Dt = Dv/a
x – x0 = v0 Dv/a + 1/2 a (Dv/a)2
2a (x–x0) = 2v0 (v–v0) + (v–v0)2
2a (x–x0) = 2vv0 – 2v02 + v2 – 2vv0 + v02
2a (x–x0) = 2vv0 – 2vv0 + v2 + v02 – 2v02
2a (x–x0) = v2 – v02
v2 = v02 + 2a (x–x0)
Do units check out?

16. Another Form (constant a)
If you don’t know a but know v, v0, and Dt:
x = x0 + v0Dt + 1/2 a (Dt)2 a = Dv/Dt = (v–v0)/Dt
x = x0 + v0 Dt + 1/2 ((v–v0)/Dt) (Dt)2
x – x0 = v0 Dt + 1/2 v Dt – 1/2 v0 Dt
x – x0 = v0 Dt – 1/2 v0 Dt + 1/2 v Dt
x – x0 = 1/2 (v0 + v) Dt
Do units check out?