The position of an object moving along a line is given by the function s(t) = -7t^2 +70t. Find the average velocity of the object over the following intervals.

Question

(a)​ [1,5]

​(b) ​[1,4​]

​(c)​ [1,3​]

​(d) ​[1, 1​+h] where h > 0 is any real number.

Answer 1

s(t) =-7t²+70t

s(1) = -7+70 = 63

s(5) = -175+350=175

s(4) = 168

s(3) = 147

a) V_avg = (s(5)-s(1))/(5-1) = (175-63)/4 = 28

b) V_avg =(s(4) - s(1))/(4-1) = (168-63)/3 = 35

c) V_avg= (s(3)-s(1))/((3-1) = (147-63)/2 = 42

d)

V_avg(h) = (s(1+h)-s(1))/(1+h-1) = (-7(1+h)²+70(1+h)+7 - 70)/h

= 56-7h

Notice that if h = t₁-t₀

_V(4) = 28, same as (a)

V(3)= 35, same as (b)

V(2)=42, same as (c)