Consider a car whose position, s, is given by the table
(s) 0 0.2 0.4 0.6 0.8 1
(ft) 0 0.3 1.4 3.8 6.5 9.6
Find the average velocity over the interval 0<=t<=0.2 (include units)
Estimate the velocity at t=0.2. (include units)
you said position s, then have a column ft. Where is time in this?
To find the average velocity over the interval 0<=t<=0.2, we need to calculate the displacement and divide it by the time taken.
The displacement is given by the difference in position between the initial and final points.
For t=0, the position is 0 ft, and for t=0.2, the position is 0.3 ft.
Displacement = 0.3 ft - 0 ft = 0.3 ft
The time taken is 0.2 seconds.
Average velocity = Displacement / Time taken
Average velocity = 0.3 ft / 0.2 s = 1.5 ft/s
Therefore, the average velocity over the interval 0<=t<=0.2 is 1.5 ft/s.
To estimate the velocity at t=0.2, we can use the concept of instantaneous velocity.
By looking at the position values in the table, we can see that the change in position from t=0.2 to t=0.4 is 1.4 ft - 0.3 ft = 1.1 ft.
The time taken is 0.4 s - 0.2 s = 0.2 s.
Instantaneous velocity = Change in position / Time taken
Instantaneous velocity = 1.1 ft / 0.2 s = 5.5 ft/s
Therefore, the estimated velocity at t=0.2 is 5.5 ft/s.
To find the average velocity over the interval 0 <= t <= 0.2, we need to use the formula:
Average velocity = (change in position) / (change in time)
To calculate the change in position, we subtract the initial position from the final position: s_final - s_initial. In this case, the initial position is given as s = 0 at t = 0 and the final position is given as s = 0.3 at t = 0.2, so the change in position is:
Change in position = 0.3 - 0 = 0.3 ft
The change in time is simply the difference in time between the final and initial positions: t_final - t_initial = 0.2 - 0 = 0.2 sec
Now we can plug these values into the formula for average velocity:
Average velocity = (0.3 ft) / (0.2 sec)
Simplifying this expression, we get the average velocity:
Average velocity = 1.5 ft/sec
Therefore, the average velocity over the interval 0 <= t <= 0.2 is 1.5 ft/sec.
To estimate the velocity at t = 0.2, we can look at the change in position over a very small time interval around t = 0.2. In this case, we can use the table to estimate the change in position between t = 0.2 and t = 0.4, which is 1.4 - 0.3 = 1.1 ft.
Since the time interval is very small (0.2 sec), we can approximate the velocity at t = 0.2 as the change in position divided by the change in time:
Velocity at t = 0.2 ≈ (1.1 ft) / (0.2 sec)
Simplifying this expression, we get the estimated velocity at t = 0.2:
Velocity at t = 0.2 ≈ 5.5 ft/sec
Therefore, the estimated velocity at t = 0.2 is 5.5 ft/sec.