a body moves on a coordinate line such that it has a position s = f(t)=t² - 7t + 6 on the interval 0 ≤ t ≤…

a body moves on a coordinate line such that it has a position s = f(t)=t² - 7t + 6 on the interval 0 ≤ t ≤ 5, with s in meters and t in seconds.\na. find the bodys displacement and average velocity for the given time interval.\nb. find the bodys speed and acceleration at the endpoints of the interval.\nc. when, if ever, during the interval does the body change direction?\nthe bodys displacement for the given time interval is - 10 m.\n(type an integer or a simplified fraction.)\nthe bodys average velocity for the given time interval is - 2 m/s.\n(type an integer or a simplified fraction.)\nthe bodys speeds at the left and right endpoints of the interval are 7 m/s and 3 m/s, respectively.\n(type integers or simplified fractions.)\nthe bodys accelerations at the left and right endpoints of the interval are 2 m/s² and 2 m/s², respectively.\n(type integers or simplified fractions.)\nwhen, if ever, during the interval does the body change direction? select the correct choice below and fill in any answer boxes within your choice.\na. the body changes direction at t = s.\n(type an integer or a simplified fraction.)\nb. the body does not change direction during the interval

a body moves on a coordinate line such that it has a position s = f(t)=t² - 7t + 6 on the interval 0 ≤ t ≤ 5, with s in meters and t in seconds.\na. find the bodys displacement and average velocity for the given time interval.\nb. find the bodys speed and acceleration at the endpoints of the interval.\nc. when, if ever, during the interval does the body change direction?\nthe bodys displacement for the given time interval is - 10 m.\n(type an integer or a simplified fraction.)\nthe bodys average velocity for the given time interval is - 2 m/s.\n(type an integer or a simplified fraction.)\nthe bodys speeds at the left and right endpoints of the interval are 7 m/s and 3 m/s, respectively.\n(type integers or simplified fractions.)\nthe bodys accelerations at the left and right endpoints of the interval are 2 m/s² and 2 m/s², respectively.\n(type integers or simplified fractions.)\nwhen, if ever, during the interval does the body change direction? select the correct choice below and fill in any answer boxes within your choice.\na. the body changes direction at t = s.\n(type an integer or a simplified fraction.)\nb. the body does not change direction during the interval

Answer

Explanation:

Step1: Recall velocity formula

Velocity $v(t)$ is the derivative of position $s(t)$. Given $s(t)=t^{2}-7t + 6$, then $v(t)=s^\prime(t)=2t - 7$.

Step2: Find when velocity is zero

Set $v(t)=0$, so $2t - 7=0$. Solving for $t$ gives $t=\frac{7}{2}=3.5$ s. But we need to check if this value is in the interval $[0,5]$. Since $3.5\in[0,5]$, the body changes direction at $t = 3.5$ s.

Answer:

A. The body changes direction at $t = 3.5$ s.