Answer
(a) v = 2.83 m/s
(b) v = 3.46 m/s
Work Step by Step
To find the work done by the force, we need to calculate the area under the F versus x graph.
(a) $W = \frac{1}{2}(10~N)(8.0~m)$
$W = 40~J$
We can use the work-energy theorem to find the speed of the sled.
$W = K_2 - K_1$
$40~J = \frac{1}{2}mv^2 - 0$
$v^2 = \frac{80~J}{10.0~kg}$
$v = \sqrt{\frac{80~J}{10.0~kg}}$
$v = 2.83~m/s$
(b) From t = 8.0 s to t = 12.0 s:
$W = \frac{1}{2}(10~N)(4.0~m)$
$W = 20~J$
We can find the total work done from t = 0 to t = 12.0 s:
$W_{tot} = 40~J + 20 ~J = 60~J$
We can use the work-energy theorem to find the speed of the sled.
$W = K_2 - K_1$
$60~J = \frac{1}{2}mv^2 - 0$
$v^2 = \frac{120~J}{10.0~kg}$
$v = \sqrt{\frac{120~J}{10.0~kg}}$
$v = 3.46~m/s$
