Answer
(a) (4) one-fourth as great.
(b) $4.0\,m/s^{2}$
Work Step by Step
(a) Newton's second law states that $F=ma$.
If $F'=\frac{F}{2}$ and $m'=2m$, Then
$a'=\frac{F'}{m'}=\frac{\frac{F}{2}}{2m}=\frac{1}{4}\times\frac{F}{m}=\frac{1}{4}a$.
The acceleration will be one-fourth if the force is halved and the mass is doubled.
(b) Given/Known: $F=ma,$ $F'=2F,$ $m'=\frac{1}{2}m,$ $a=1.0\,m/s^{2}$
We need to find $a'$ which is equal to $\frac{F'}{m'}$
$a'=\frac{2F}{\frac{m}{2}}=4\times\frac{F}{m}=4\times a=4\times1.0\,m/s^{2}=4.0\,m/s^{2}$
