#### Answer

(a) v = 2.0 m/s
(b) v = 2.0 m/s
(c) v = 1.73 m/s

#### Work Step by Step

To find the work done by the force, we can calculate the area under the Force versus x graph.
(a) From x = 0 to x = 3.0 m:
W = 2.0 J + 2.0 J = 4.0 J
We can use the work to find the speed $v$.
$K_2 - K_1 = W$
$\frac{1}{2}mv^2 - 0 = 4.0~J$
$v^2 = \frac{8.0~J}{m}$
$v = \sqrt{\frac{8.0~J}{2.0~kg}}$
$v = 2.0~m/s$
(b) From x = 0 to x = 4.0 m:
W = 2.0 J + 2.0 J + 0 = 4.0 J
We can use the work to find the speed $v$.
$K_2 - K_1 = W$
$\frac{1}{2}mv^2 - 0 = 4.0~J$
$v^2 = \frac{8.0~J}{m}$
$v = \sqrt{\frac{8.0~J}{2.0~kg}}$
$v = 2.0~m/s$
(c) From x = 0 to x = 7.0 m:
W = 2.0 J + 2.0 J + 0 - 1.0 J= 3.0 J
We can use the work to find the speed $v$.
$K_2 - K_1 = W$
$\frac{1}{2}mv^2 - 0 = 3.0~J$
$v^2 = \frac{6.0~J}{m}$
$v = \sqrt{\frac{6.0~J}{2.0~kg}}$
$v = 1.73~m/s$