Sept. 11 – Formative Quiz and VT Graphs

Today we did our formative quiz and took it up in class.

• Formative Quiz Solutions

Then we discussed VT graphs...

Velocity Time Graphs

Graphs with v on the y-axis, t on the x-axis

Example: Graph of wandering dog.

Question: What is the dog's displacement?

Answer: v = ∆d / ∆t  —> ∆d = v ∆t

• v ∆t is the AREA under the vt graph.
• displacement is the AREA between the vt graph and the x-axis.

Break up the area into 4 sections and calculate the area of each section.

d1 = (1 m/s)(4 s) = 4 m

d2 = (1 m/s)(2 s) ÷ 2 = 1 m

d3 = (-2 m/s)(4 s) ÷ 2 = -4 m

d4 = (-2 m/s)(3 s) = -6 m

∆d = d1 + d2 + d3 + d4

     = 4m +1m – 4m –6m

     = -5 m

Example:  What is the dog’s average velocity?

Average velocity = total displacement ÷ total time

v(average) = -0.4 m/s [forward]

Instantaneous Velocity

The velocity at any instant of time.

Examples:

The dog’s instantaneous velocity at 5s is 0.5 m/s [forward].

The dog’s instantaneous velocity at 12 s is -2 m/s [forward]. 

MORE ON VECTORS

Look at Monopoly board.

Write a vector that goes from “Free Parking” to “Jail”.

    A = 10 steps [down]

Challenge: Write a vector that goes from “Water Works” to “Jail”.