Question 6ca10

Jun 29, 2017

$78 \text{ m}$.

Explanation:

Given function is

$s \left(t\right) = 5 {t}^{2} + t + 2$

Distance covered in $t = 1 \text{ s}$
s(1)=5(1)²+(1)+2=8" m"

Distance covered in $t = 4 \text{ s}$
s(4)=5(4)²+(4)+2=86" m"

Distance covered in the given time interval $= 86 - 8 = 78 \text{ m}$

Jun 29, 2017

$78$ $\text{m}$

Explanation:

We're given an equation for distance, and we're asked to find the distance traveled on the interval $t \in \left[1 \textcolor{w h i t e}{l} \text{s", 4color(white)(l)"s}\right]$.

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 $t = 1$ $\text{s}$ to $t = 4$ $\text{s}$, the object traveled a distance of color(blue)(78 sfcolor(blue)("meters"#.