suppose the position of an object moving in a straight line is given by s(t)=3t² + 5t + 2. find the…

suppose the position of an object moving in a straight line is given by s(t)=3t² + 5t + 2. find the instantaneous velocity when t = 6. what expression can be used to find the instantaneous velocity at the given time? a. (s(6)-s(0))/(6 - 0) b. (s(6)+s(0))/(6 + 0) c. lim(h→0) (s(6 + h)-s(6))/h d. lim(b→a) (s(6)-s(a))/(6 - a)

suppose the position of an object moving in a straight line is given by s(t)=3t² + 5t + 2. find the instantaneous velocity when t = 6. what expression can be used to find the instantaneous velocity at the given time? a. (s(6)-s(0))/(6 - 0) b. (s(6)+s(0))/(6 + 0) c. lim(h→0) (s(6 + h)-s(6))/h d. lim(b→a) (s(6)-s(a))/(6 - a)

Answer

Explanation:

Step1: Recall velocity - definition

The instantaneous velocity of an object at time (t = a) is given by the limit formula (v(a)=\lim_{h\rightarrow0}\frac{s(a + h)-s(a)}{h}). Here (a = 6), so the formula for the instantaneous velocity at (t = 6) is (\lim_{h\rightarrow0}\frac{s(6 + h)-s(6)}{h}).

Answer:

C. (\lim_{h\rightarrow0}\frac{s(6 + h)-s(6)}{h})