The ants of the North Creek Ant Colony traverse a straight trail between their colony and a nearby picnic table. One ant, returning after quenching its thirst with a portion of a tasty beverage dripping from the table, is first observed along the trail 3.1 m from the colony. Then, after traveling a total of 2.6 m while staggering back and forth along the trail, the ant falls unconscious 1.3 m from the colony exactly 43 s later.
Defining the entrance of the colony as the origin and the positive direction toward the picnic table, determine the ant's average velocity 𝑣avg during this time interval.
avg velocity = displacement/time = (1.3-3.1)/43 = -0.04186 m/s
the 2.6m traveled only affects the speed, not the velocity.
Well the average velocity is the displacement divided by the time
unlike the
average speed which is the distance divided by the time
displacement includes direction and the direction is negative, toward home from the table
so the displacement was - (3.1 - 1.3) = - 1.8
so velocity is -1.8 / 43 m/s = - 0.0232 m/s or -2.32 cm/s (almost -an inch a second)
whoops, divided wrong, - 0.041860 m/s
To determine the ant's average velocity during this time interval, we need to calculate the total displacement and divide it by the total time taken.
The total displacement is the difference between the ant's initial position and final position. In this case, the ant starts 3.1 m from the colony (initial position) and falls unconscious 1.3 m from the colony (final position). Therefore, the total displacement is:
Displacement = Final Position - Initial Position
Displacement = 1.3 m - (-3.1 m)
Displacement = 1.3 m + 3.1 m
Displacement = 4.4 m
The total time taken is given as 43 seconds.
Now we can calculate the average velocity using the formula:
Average Velocity = Displacement / Time
Average Velocity = 4.4 m / 43 s
To get the average velocity, divide the displacement by the time taken.
Average Velocity ≈ 0.102 m/s
Therefore, the ant's average velocity during this time interval is approximately 0.102 m/s.