Question

A bug is moving along a straight path with velocity v(t)= t^2-6t+8 for t ≥0. Find the total distance traveled by the bug over interval [0,6].

Answer 1

Step-by-step explanation

Given:

A bug is moving along a straight path with velocity

`V(t)=t^2-6t+8\text{ }for\text{ }t>0`

What to find:

The total distance traveled by the bug over interval [0, 6].

Solution:

To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8

`\begin{gathered} \int_0^6t^2-6t+8 \\ \\ [(t^3)/(3)-(6t^2)/(2)+8t]^6_0 \\ \\ ((t^3)/(3)-3t^2+8t)^6-((t^(3))/(3)-3t^2+8t)^0 \\ \\ ((6^3)/(3)-3(6)^2+8(6))-((0^3)/(3)-3(0)^2+8(0)) \\ \\ ((216)/(3)-3(36)+48)-(0-0+0) \\ \\ 72-108+48-0 \\ \\ =12\text{ }units \end{gathered}`