Speedometer readings for a motorcycle at $12-$second intervals are given in the table.

$\backslash$table$[[t(s),0,12,24,36,48,60],[v(f\frac{t}{s}),32,28,25,22,25,28]]$

$($a$)$ Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals. $ft$

$($b$)$ Give another estimate using the velocities at the end of the time periods. ft

$($c$)$ Are your estimates in parts $($a$)$ and $($b$)$ upper and lower estimates? Explain.

$($a$)$ and $($b$)$ are neither lower nor upper estimates since $v$ is neither an increasing nor decreasing function of $t.$

$($a$)$ is a lower estimate and $($b$)$ is an upper estimate since $v$ is an increasing function of $t.$

$($b$)$ is a lower estimate and $($a$)$ is an upper estimate since $v$ is a decreasing function of $t.$