Question 4
A rocket travels at velocity given by $v(t)$, and is always accelerating (speeding up). Let $v$ be measured in m/s, and time $t$ in seconds.
Which of the following would be the most accurate overestimate of the distance traveled by the rocket in the first two seconds of flight? ($t=0$ is launch time.)
$2v(2)$
$v(0) + v(1)$
$2v(0)$
$v(0) + v(1) + v(2)$
$v(1) + v(2)$
Feedback
If the rocket is speeding up, then the highest velocity occurs at the end of each interval, so
distance traveled between $t=0$ and $t=1$ is less than $v(1) m/s \cdot 1s = v(1) m$
distance traveled between $t=1$ and $t=2$ is less than $v(2) m/s \cdot 1s = v(2) m$