Answer
a. they are equal
b. III is best
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
a.
The same net force causes momentum change in both cases, so, in that (same) time period, the boulder and the pebble experience the same rate of change of momentum.
b.
As seen above, explanation III is best -- equal force means equal change in momentum for a given time.
I is not correct, as the speed gained will be relatively small.
II is correct as far as speed goes, but because of smaller mass, the change in momentum is the same.
