Question

Question #6ca10

Answer 1

`78" m"`.

Explanation:

Given function is

`s(t)=5t^2+t+2`

Distance covered in `t=1" s"`
`s(1)=5(1)²+(1)+2=8" m"`

Distance covered in `t=4" s"`
`s(4)=5(4)²+(4)+2=86" m"`

Distance covered in the given time interval `=86-8=78" m"`

Answer 2

`78` `"m"`

Explanation:

We're given an equation for distance, and we're asked to find the distance traveled on the interval `t in [1color(white)(l)"s", 4color(white)(l)"s"]`.

To do this, let's find the distance covered at each of these times, and find the difference between them.

Plugging in `1` for `t`:

`s(1) = 5(1)^2 + (1) + 2 = color(red)(8` `color(red)("m"`

And then plugging in `4`:

`s(4) = 5(4)^2 + (4) + 2 = color(green)(86` `color(green)("m"`

The distance it traveled in this time interval is thus

`"Distance" = s(4) - s(1) = color(green)(86` `color(green)("m"` `- color(red)(8` `color(red)("m"` `= color(blue)(78` `color(blue)("m"`

Thus from time `t = 1` `"s"` to `t = 4` `"s"`, the object traveled a distance of `color(blue)(78` `sfcolor(blue)("meters"`.