If the work to be done is rectilinear motion of a body with constant mass m {\displaystyle m\;} , whose center of mass is to be accelerated along a straight line to a speed | v ( t ) | {\displaystyle |\mathbf {v} (t)|\;} and angle ϕ {\displaystyle \phi \;} with respect to the centre and radial of a gravitational field by an onboard powerplant, then the associated kinetic energy to be delivered to the body is equal to