Question

Answer Check!! Medal!!
For an object whose velocity in ft/sec is given by v(t) = −2t2 + 8, what is its distance travelled, in feet, on the interval t = 0 to t = 3 secs?

6.00 <---
0.67
15.33
5.11

Answer 1

@jim_thompson5910

Answer 2

incorrect

a graph may help show you why it's a bad idea to just integrate from 0 to 3

Answer 3

keep in mind that `total distance` is NOT the same as `displacement`

Answer 4

so you want me to graoh -2t+8

Answer 5

it's -2t^2 + 8 right?

Answer 6

yeah that's what i meant

Answer 7

yes graph that

Answer 8

ok

Answer 9

tell me what the x intercepts are

Answer 10

(-2,0) and (2,0)

Answer 11

correct. The root (2,0) will help you break up the integral into 2 pieces

Let
A = area of red region
B = area of green region
See attached


Notice how the green region is below the x axis, so it will have negative area


To find the total distance, we use absolute values to ensure we're adding the positive versions of the areas


total distance = |A| + |B|

Answer 12

the red region represents the object moving forward some distance (since the area is above the x axis, it's positive)

the green region represents the object moving backwards some other distance

adding up the positive and negative areas, ie integrating from 0 to 3, yields the displacement of 6. This isn't the answer since they want the total distance traveled

Answer 13

so I add the areas of the red and green regions

Answer 14

yes the absolute values of each