Final answer:
The change in kinetic energy of the proton is found by calculating the initial and final kinetic energies using the work-energy theorem and the kinetic energy formula. After determining the final velocity with the kinematic equation, the difference between the final and initial kinetic energies gives the change in kinetic energy.
Step-by-step explanation:
To calculate the change in kinetic energy of a proton accelerated through a distance of 3.5 cm with an initial velocity of 2.4×107 m/s and an acceleration of 3.6×1015 m/s2, we can use the work-energy theorem. This theorem states that the net work done on an object is equal to the change in its kinetic energy. The net work done on the proton is equivalent to the force acting on it times the distance over which the force acts.
First, we calculate the final velocity using the kinematic equation v2 = u2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. The final velocity comes out to be v = √(2.4×107 m/s)2 + 2×3.6×1015 m/s2×0.35 m). After finding v, we can use the kinetic energy formula (KE = 0.5×m×v2) to find both the initial and final kinetic energies.
The change in kinetic energy is the final kinetic energy minus the initial kinetic energy. With the proton's mass of 1.67×10−27 kg, the initial kinetic energy (KEi) can be calculated and so can the final kinetic energy (KEf). The difference in kinetic energies will give us the answer.