Work, energy and power

For a constant force $F$ and straight displacement $d$, the work done is $W=Fd\cos\theta$, where $\theta$ is the angle between force and displacement. A force along the motion does positive work; a force opposite it does negative work. A perpendicular force does no work. Work is measured in joules: $1\,\mathrm{J}=1\,\mathrm{N\,m}$. The work-energy theorem uses net work, so include gravity, resistance and any applied forces as appropriate. Avoid multiplying a force by the total path length if that force does not act along the path.

Kinetic energy is $K=\tfrac12 mv^2$. Near Earth's surface, gravitational potential energy relative to a chosen reference height is $U_g=mgh$. If only gravity does work, $K_i+U_i=K_f+U_f$. With resistance, mechanical energy decreases by the positive magnitude of the energy dissipated. Equivalently, $K_i+U_i+W_{\mathrm{nc}}=K_f+U_f$, where $W_{\mathrm{nc}}$ is the work of non-conservative forces and is negative for friction. Energy is conserved overall, but some mechanical energy becomes thermal energy. State the reference height consistently.

Average power is energy transferred divided by elapsed time, $P_{\mathrm{avg}}=\Delta E/\Delta t$. Its SI unit is the watt, with $1\,\mathrm{W}=1\,\mathrm{J/s}$. For a moving object, the instantaneous power delivered by a force is $P=\mathbf F\cdot\mathbf v$. The force must be taken along the velocity direction for positive delivered power. A resistive force does negative mechanical work, but the rate of energy dissipated is usually reported as a positive number. Check what the question means by power before assigning a sign.