Show how the alternative definition of power, found in your book, can be derived by substituting the definitions of work and speed into the standard

definition of power, P = W / delta t

Power formula is P = W / Delta t, or we know that W = saclar product of D and F, D=length of distance traveled, F = the applied force, it is W = / / D / / / / F / / cos (D, F), when we substitute, we get P=[ / / D / / / / F / / cos (D, F) ] / deltat, or / / D / / = V x delta t, P = [V x delta t x / / F / / cos (D, F) ] / delta t, and then P = V//F//cos (D, F), or V and D have the same direction, so cos (D, F) = cos (V, F), finally P = V. F (or scalar product of V and F)