An ice block floating in a river is pushed through a displacement $\overrightarrow{d}=\left(20 \mathrm{m}\right)\hat{\mathrm{i}}-\left(16 \mathrm{m}\right)\hat{\mathrm{j}}$ along a straight embankment by rushing water, which exerts a force $\overrightarrow{F}=\left(210 \mathrm{N}\right)\hat{\mathrm{i}}-\left(150 \mathrm{N}\right)\hat{\mathrm{j}}$ on the block. How much work does the force do on the block during the displacement?

A particle travels through a three-dimensional displacement given by $\overrightarrow{\mathit{d}}=\left(5.00\hat{\mathrm{i}}-3.00\hat{\mathrm{j}}+4.00\hat{\mathrm{k}}\right) \mathrm{m}.$ If a force of magnitude
$22.0 \mathrm{N}$ and with fixed orientation does work on the particle, find the angle between the force and the displacement if the change in the particle's kinetic energy is (a) $45.0 \mathrm{J}$ and (b) $-45.0 \mathrm{J}$. 

A can of bolts and nuts is pushed $2.00 \mathrm{m}$along the $x$-axis by a broom along a greasy (frictionless) floor of a car repair shop in a version of shuffleboard. The figure shown below gives the work $W$ done on the can by the constant horizontal force from the broom versus the can's position $x$. The scale of the figure's vertical axis is set by, $W_{\mathrm{s}}=6.0 \mathrm{J}$.

(a) What is the magnitude of that force?
(b) If the can had an initial kinetic energy of $3.00 \mathrm{J}$ moving in the positive direction of the $x$-axis, what is its kinetic energy at the end of $2.00 \mathrm{m}$?

The figure shown below shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but now moves across a frictionless floor. The force magnitudes are ${\mathrm{F}}_1=3.00 \mathrm{N},{\mathrm{F}}_2=4.00 \mathrm{N}$ and ${\mathrm{F}}_3=9.00 \mathrm{N},$ and the indicated angles are ${\mathrm{\theta }}_2=50.0°$, ${\mathrm{\theta }}_3=35.0°$. What is the net work done on the canister by the three forces during the first $4.00 \mathrm{m}$ of displacement?

(Given:- $\sin \left(50°\right)=0.766\text{ and} \sin \left(35°\right)=0.57$)

In the figure shown below the three forces applied to a trunk that moves leftward by $3.00 \mathrm{m}$ over a frictionless floor. The force magnitudes are $F_1=5.00 \mathrm{N}, F_2=9.00 \mathrm{N}$ and $F_3=3.00 \mathrm{N}$ and the indicated angle is $\text{θ}=60.0°.$ During the displacement,
(a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease?

A $7.0 \mathrm{kg}$ object is moving in the positive direction of an $x$-axis. When it passes through $x=0$, a constant force directed along the axis begins to act on it. The figure shown below gives its kinetic energy $K$ versus position $x$, as it moves from $x=0$ to $x=5.0 \mathrm{m}$,$K_0=30.0 \mathrm{J}$. The force continues to act. What is $v$ when the object moves back through $x=-3.0 \mathrm{m}$?