Answer
a. The boulder's change in speed is less than the pebble's.
b. Best: I
Work Step by Step
In terms of momentum, Newton's second law is
$\displaystyle \sum\vec{\mathrm{F}}=\frac{\Delta\vec{\mathrm{p}}}{\Delta t} \qquad$9-3
The linear momentum of an object of mass $m$ moving with velocity $\vec{\mathrm{v}}$ is
$\vec{\mathrm{p}}=m\vec{\mathrm{v}} \qquad $9-1
Linear momentum is a vector, pointing in the same direction as the velocity vector, $\vec{\mathrm{v}}$.
$a.$
The same net force causes momentum change in both cases (9-3).
$\Delta p_{1}=\Delta p_{2}\Rightarrow m\Delta v_{1}=m_{2}\Delta v_{2}$
$\displaystyle \frac{\Delta v_{1}}{\Delta v_{2}}=\frac{m_{2}}{m_{1}}=\frac{1}{m_{1}/m_{2}}$
The less massive object will experience a greater change of speed than the more massive object.
The boulder's change in speed is less than the pebble's.
$b.$
I: true
II: the change in force results in change of momentum, not speed, so this is incorrect.
III: yes, but it has no bearing on the question.
Best: I