Question

a body moves on a coordinate line such that it has a position s=f(t)=t^2-8t+7 on the interval 0(greater than or equal to)t(greater than or equalto)9 with s in meters and t in seconds

a)find the bodys displacement and average velocity for the given time interval
b)find the bodys speed and acceleration at the endpoints of the interval
c)when,if ever,during the interval does the body change direction?

section 3.4

Answer 1

a. the displacement is simply the interval
f(9)-f(0) = (81-72+7) - (7) = 16 -7 = 9 m
average velocity = distance/time = (f(9)-f(0))/Δt = = (16-7)/9 = 1 m/s

b. taking the derivative of our f(t) we obtain the velocity function:
v(t) = 2t-8
at the endpoint of the interval
v(t) = v(9) = 18-8 = 10 m/s
taking the derivative of our v(t) we obtain the acceleration function:
a(t) = 2
at the endpoint of the interval
a(t) = a(9) = 2 m/s^2

c. the body changes direction when the velocity is momentarily 0; set v(t) = 0

v(t) = 2t-8 = 0

t = 4 seconds