Question

use the graph to determine the velocity between 6 and 12 seconds.
what was the velocity over the entire trip?

Explanation:

First Question: Velocity between 6 and 12 seconds

Step1: Recall velocity formula

Velocity \( v = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is change in position, \( \Delta t \) is change in time.

Step2: Identify positions and times

At \( t = 6 \) s, position \( x_1 = 12 \) m. At \( t = 12 \) s, position \( x_2 = 0 \) m. \( \Delta t = 12 - 6 = 6 \) s, \( \Delta x = 0 - 12 = -12 \) m.

Step3: Calculate velocity

\( v = \frac{-12}{6} = -2 \) m/s. (Negative sign indicates direction, but magnitude or with sign as per graph.)

Step1: Recall velocity formula

\( v = \frac{\Delta x}{\Delta t} \).

Step2: Identify total change in position and time

Initial position \( x_i = 0 \) m, final position \( x_f = 0 \) m. Total time \( \Delta t = 12 - 0 = 12 \) s. \( \Delta x = 0 - 0 = 0 \) m.

Step3: Calculate velocity

\( v = \frac{0}{12} = 0 \) m/s.

Answer:

-2 (or 2 if considering speed, but velocity includes direction; from graph, it's -2 m/s)

Second Question: Velocity over entire trip (0 to 12 seconds)