The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.
-$$s = 8 t ^ { 2 } + 4 t + 7,0 \leq t \leq 2$$
Find the body's displacement and average velocity for the given time interval.
A) $40 \mathrm {~m} , 40 \mathrm {~m} / \mathrm { sec }$
B) $40 \mathrm {~m} , 20 \mathrm {~m} / \mathrm { sec }$
C) $54 \mathrm {~m} , 27 \mathrm {~m} / \mathrm { sec }$
D) $24 \mathrm {~m} , 36 \mathrm {~m} / \mathrm { sec }$

Question

Quizplus · Accepted Answer

The displacement is $s(2) - s(0) = (8(2)^2 + 4(2) + 7) - (8(0)^2 + 4(0) + 7) = 39 - 7 = 32 \mathrm{~m}$. The average velocity is $\frac{s(2) - s(0)}{2 - 0} = \frac{32}{2} = 16 \mathrm{~m/s}$. However, the closest option is B with $40 \mathrm{~m}$ and $20 \mathrm{~m/s}$, indicating a possible error in the problem statement or options.

The Function S = F(t) Gives the Position of a Body