A body moves on a coordinate line such that it has a position sequals​f(t)equalstsquaredminus4tpl us3on the interval 0less than or equalstless than or equals7​,with s in meters and t in seconds. a. Find the​ body's displacement and average velocity for the given time interval. b. Find the​ body's speed and acceleration at the endpoints of the interval. c.​ When, if​ ever, during the interval does the body change​ direction?

A)  Δf = - 49 m, B)  v (7)  = -56 m / s, a = - 8 m / s², C)  t = 0.866 s

Explanation:

A) In this exercise ask to find the displacement and the average velocity, give the function of the movement

           f (t) = - 4t² +3

and the range of motion 0≤ t ≤ 7

the displacement is

for t = 0

           f (0) = 3

for t = 7 s

           f (7) = - 4 7² +3

           f (7) = -46 m

the total displacement is

           Δf = f (7) - f (0)

           Δf = -46 - 3

            Δf = - 49 m

the average speed is defined as the displacement between the time interval

           v = Df / Dt

           v = -49 / 7

           v = - 7 m / s

B) the speed and acceleration of the end points of the motion

the speed of defined by

          v =

in this case

         v =

         v = -8t

let's calculate

          v (7) = -8 7

          v (7)  = -56 m / s

acceleration is defined by

          a =

          a = - 8 m / s²

acceleration is constant throughout the movement

C) the point where the direction changes.

This point is a point where the position goes from positive to negative, the point f = 0

        0 = -4t² +3

        t = √¾

        t = 0.866 s

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force