QuestionFind the average velocity of an object from $2 \leq t \leq 4$ and from $1 \leq t \leq 5$ using $y=s(t)$ data.

Studdy Solution

STEP 1

Assumptions1. The height of the object at different time points is given in the table. . The average velocity is calculated as the change in position (height) divided by the change in time.

STEP 2

To find the average velocity over the interval $2 \leq t \leq4$ , we need to subtract the height at $t=2$ from the height at $t=4$ and divide by the difference in time.
$AV_{[2,4]} = \frac{y(4) - y(2)}{4 -2}$

STEP 3

Now, plug in the given values for the heights at $t=2$ and $t=$ to calculate the average velocity.
$AV_{[2,]} = \frac{67 -53}{ -2}$

STEP 4

Calculate the average velocity over the interval $2 \leq t \leq4$ .
$AV_{[2,4]} = \frac{67 -53}{4 -2} =7 \, \text{meters/minute}$

STEP 5

To find the average velocity over the interval $1 \leq t \leq5$ , we need to subtract the height at $t=1$ from the height at $t=5$ and divide by the difference in time.
$AV_{[1,5]} = \frac{y(5) - y(1)}{5 -1}$

STEP 6

Now, plug in the given values for the heights at $t=1$ and $t=5$ to calculate the average velocity.
$AV_{[1,5]} = \frac{18 -35}{5 -1}$

STEP 7

Calculate the average velocity over the interval $1 \leq t \leq5$ .
$AV_{[1,5]} = \frac{18 -35}{5 -1} = -4.25 \, \text{meters/minute}$ The average velocity of the object over the interval $2 \leq t \leq4$ is $7$ meters/minute and over the interval $1 \leq t \leq5$ is $-4.25$ meters/minute. The negative sign indicates that the object is moving downwards.

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