Question

1. write the equation for average velocity and define all the variables. 12. sloth feed and live on cecropia trees which grow to an average height of 49 feet. if a sloth climbs from the bottom of the tree to the top with an average velocity of 0.22 $\frac{ft}{s}$, how much time does it take to reach the bottom?

Explanation:

Question 11

Step1: Recall average velocity formula

The formula for average velocity ($v_{avg}$) is the displacement ($\Delta x$) divided by the time interval ($\Delta t$) over which the displacement occurs. So the equation is $v_{avg} = \frac{\Delta x}{\Delta t}$.

Step2: Define variables

• $v_{avg}$: Represents the average velocity of an object. It is a vector quantity (in the context of displacement) but can be treated as a scalar for one - dimensional motion with constant direction, and its units depend on the units of displacement and time (e.g., meters per second, feet per second).
• $\Delta x$: Represents the displacement of the object. Displacement is the change in position of the object, i.e., the final position minus the initial position ($\Delta x=x_f - x_i$), and its units are units of length (e.g., meters, feet).
• $\Delta t$: Represents the time interval during which the displacement occurs. It is the final time minus the initial time ($\Delta t=t_f - t_i$), and its units are units of time (e.g., seconds, minutes).

Step1: Identify the formula to use

We know the formula for average velocity $v_{avg}=\frac{\Delta x}{\Delta t}$. We need to solve for time $t$ (here $\Delta t$ is the time we want to find, and since the sloth moves from the bottom to the top, the displacement $\Delta x$ is equal to the height of the tree, which is 49 feet, and the average velocity $v_{avg} = 0.22\frac{ft}{s}$). Rearranging the formula for $\Delta t$, we get $\Delta t=\frac{\Delta x}{v_{avg}}$.

Step2: Substitute the values

We have $\Delta x = 49\ ft$ and $v_{avg}=0.22\ \frac{ft}{s}$. Substituting these values into the formula $\Delta t=\frac{\Delta x}{v_{avg}}$, we get $\Delta t=\frac{49}{0.22}$.

Step3: Calculate the value

$\frac{49}{0.22}\approx222.73\ s$ (we perform the division: $49\div0.22\approx222.73$).

Answer:

The equation for average velocity is $v_{avg}=\frac{\Delta x}{\Delta t}$, where $v_{avg}$ is the average velocity, $\Delta x$ is the displacement, and $\Delta t$ is the time interval.

Question 12