Question

Help!!!

Answer 1

The function \[s=-t^3+6t^2-12t, 0\le3\] gives the position of a body moving on a coordinate line, with s in meters and t in seconds.
a. Find the body's displacement and average velocity for the given time interval
b. Find the body's speed and acceleration at the endpoints of the interval
c. When, if ever, during the interval does the body change direction

Answer 2

Did you take the first derivative of the distance function which would be the velocity function?

Answer 3

\[-3t^2+12t-12\]

Answer 4

a. Find the position at 0 and at 3 and subtract to find the displacement for the interval

Answer 5

-9?

Answer 6

That's what I got.

Answer 7

Find velocity at beginning and end of interval, subtract, divide by 3 to get average velocity

Answer 8

how?

Answer 9

What is the velocity function?

Answer 10

\[-3t^2+12t-12\]

Answer 11

What is the velocity at t = 0?

Answer 12

-12

Answer 13

What is the velocity at t = 3?

Answer 14

-3

Answer 15

What is -3minus -9?

Answer 16

6

Answer 17

Whoops. What is -3 minus -12 I should have said.

Answer 18

9

Answer 19

What is 9 divided by 3?

Answer 20

3

Answer 21

ok. average velocity : (velocity at end of interval - velocity at beginning of interval) divided by length of interval

Answer 22

Now b. You've already found the velocity at the beginning and end of the interval. The acceleration is the second derivative of the distance function which is the first derivative of the velocity function so find the acceleration function.

Answer 23

-6t+12

Answer 24

Plug in 0 and 3 to find the acceleration at the beginning and end of the interval

Answer 25

Did you get 12 and -6?

Answer 26

yes

Answer 27

Now,c. When does it change direction. The position function would have a high point or a low point if direction changed. That means the slope of the tangent at that point would be 0. So take the slope function, which is the first derivative, which is the velocity function, and set it equal to 0 and solve to see if there is any t value between 0 and 3 at which the slope is 0

Answer 28

at 2?