Final answer:
The speed of a proton accelerated through a potential difference of 8.0 kV is found by equating the electric potential energy gained to the kinetic energy of the proton, using the equation qV = (1/2)mv^2 and solving for v.
Step-by-step explanation:
To determine the speed of a proton that has been accelerated from rest through a potential difference of 8.0 kV, we can use the concept of energy conservation and the relationship between electric potential and kinetic energy. The electric potential energy (EPE) gained by the proton as it accelerates through the potential difference will equal its kinetic energy (KE) when it comes to rest:
EPE = KE
qV = (1/2)mv^2
Where q is the charge of the proton (1.6 × 10^-19 C), V is the potential difference (8.0 × 10^3 V), m is the mass of the proton (1.67 × 10^-27 kg), and v is the final velocity of the proton. Solve this equation for v to find the proton's final speed.