A squirrel falls from a very tall tree. Initially (at t=0 ),...

A squirrel falls from a very tall tree. Initially (at $t=0$ ), the squirrel is at the top of the tree, a distance $y=50$ m above the ground. At $t=1.0 \mathrm{s}$, the squirrel is at $y=45 \mathrm{m},$ and at $t=2.0 \mathrm{s}$ it is at $y=30 \mathrm{m} .$ Estimate the average velocity of the squirrel during the intervals from $t=0.0 \mathrm{s}$ to $t=1.0 \mathrm{s}$ and from $t=1.0 \mathrm{s}$ to $t=2.0 \mathrm{s}$. Use these results to estimate the average acceleration of the squirrel during this time. (No squirrels were harmed during the writing of this problem.)

A squirrel falls from a very tall tree. Initially (at $t=0$ ), the squirrel is at the top of the tree, a distance $y=50$ m above the ground. At $t=1.0 \mathrm{s}$, the squirrel is at $y=45 \mathrm{m},$ and at $t=2.0 \mathrm{s}$ it is at
$y=30 \mathrm{m} .$ Estimate the average velocity of the squirrel during the intervals from $t=0.0 \mathrm{s}$ to $t=1.0 \mathrm{s}$
and from $t=1.0 \mathrm{s}$ to $t=2.0 \mathrm{s}$. Use these results to estimate the average acceleration of the squirrel during this time. (No squirrels were harmed during the writing of this problem.)

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Key Concepts

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. It involves calculating the difference in the object's positions over a specific time interval and then dividing that difference by the length of the interval. This concept is important in kinematics for understanding how fast an object is moving in a particular direction over a time period.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time over which the change occurs. This concept is used in kinematics to quantify how quickly an object's velocity is changing over time. Calculating average acceleration helps in understanding whether the object is speeding up or slowing down and by how much during a specific interval.

Displacement

Displacement is the overall change in position of an object from its initial position to its final position, and it takes direction into account. In the study of motion, displacement provides the basis for calculating both average velocity and average acceleration, as it directly represents the net distance moved in a particular direction over time.

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