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

An alligator swims to the left with a constant velocity of 5 \,\dfrac{\text{m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction. when the alligator sees a bird straight ahead, the alligator speeds up with a constant acceleration of 3 \,\dfrac{\text {m}}{\text s^2}3 s 2 m ? 3, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward until it reaches a final velocity of 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction leftward. how many seconds does it take the alligator to speed up from 5 \,\dfrac{\text {m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction to 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction?

Determine the fraction of the magnitude of kinetic energy lost by a neutron (m1 = 1.01 u) when it collides head-on and elastically with a target particle at rest which is 21h (heavy hydrogen, m = 2.01 u).

Acyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with total mass 3.34×10−27kg. the deuterons exit the cyclotron with a kinetic energy of 6.40 mev .a-what is the speed of the deuterons when they exit? b-if the magnetic field inside the cyclotron is 1.25 t, what is the diameter of the deuterons' largest orbit, just before they exit? c-if the beam current is 350 μa how many deuterons strike the target each second?