A particle moves according to the equation x = 10+2, where x is in meters and t is in seconds. (a). Find the average velocity for the time interval from 2.00 s to 3.00 S. (b). Find the average velocity for the time interval from 2.00 s to 2.10 s. Hints: Make a table with columns t and x for the values t=2.00s, 2.10s, and 3.00 s and evaluate corresponding x values by substituting t values in the given equation. Use the average velocity formula Ux, avg Ay and evaluate the corresponding average velocity for the time intervals for (a) and (b).

The average velocity of a particle moving according to the equation x = 10 + 2t from 2.00 s to 3.00 s is 2m/s. Additionally, the average velocity from 2.00 s to 2.10 s is also 2m/s.

Explanation:

Given the equation for the particle's motion, x = 10 + 2t, we can find the average velocity using the formula: Ux, avg = Δx / Δt. Let's create a table with the given time values (t=2.00s, 2.10s, and 3.00s).

Let's evaluate the corresponding x values:
For t=2.00s, x = 10 + 2*2 = 14 m.
For t = 2.10s, x = 10 + 2*2.10 = 14.20 m.
For t = 3.00s, x = 10 + 2*3 = 16 m.

(a) Now compute the average velocity for the time interval from 2.00 s to 3.00 s.
Ux, avg = (16 - 14) / (3.00 - 2.00) = 2m/s.

(b) Now compute the average velocity for the time interval from 2.00 s to 2.10 s.
Ux, avg = (14.20 - 14) / (2.10 - 2.00) = 2m/s.

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