Question

Find the average velocity of the dot between t=0 and t=2. Give your answer as a pair of components.

Answer 1

The average velocity between t=0 and t=2 seconds requires the position function, which is not provided. If available, the position at both times should be calculated, the change in position found, and divided by the time interval to find the velocity components.

Step-by-step explanation:

The average velocity of a dot between t=0 and t=2 seconds can be found by calculating the change in the position vector over the time interval and dividing it by the time taken. Unfortunately, the position function for the dot is not provided in the question. However, if you have the position function ℝ(t), in the format ℝ(t) = xt(t)î + yt(t)ï, you would substitute t=2 and t=0 into it to find the positions at those times and then find the difference between the two. Once you have the change in position for both x and y components, divide each by the time interval, which is 2 seconds in this case. The resulting components will give you the average velocity as a pair of components in the form (vx, vy).

Answer 2

To find the average velocity between t=0 and t=2, one must calculate the change in position between these times and divide by the time interval. Exact numerical values for the average velocity components cannot be provided without the specific position function or formula.

Step-by-step explanation:

To find the average velocity of the dot between t=0 and t=2, we need to calculate the displacement over that time interval and then divide by the time interval. From the statements provided, it seems that we need to apply given formulas to calculate the position of the dot at both t=0 and t=2, and then use the calculated positions to find the average velocity. Without the specific formulas or position function given in the question, we cannot provide the numerical components of the average velocity. However, we know that the average velocity is calculated using the formula Vavg = (r(t2) - r(t1)) / (t2 - t1), where r(t) denotes the position vector at time t, and t1 and t2 are the initial and final times of the interval.