The nucleus of a helium atom travels along the inside of a straight hollow tube 4 ~m long which forms part of a particle accelerator. If one assumes uniform acceleration, how long is the particle in the tube if it enters at a speed of 2000 ~m / s and leaves at 8000 ~m / s

Step-by-step solution

Given the length of the tube s = 4 m , the initial velocity u = 2000 m/s , and the final velocity v = 8000 m/s . Assuming uniform acceleration, the average velocity v_ avg is given by the formula v_ avg = u + v 2 . Substituting the given values, v_ avg = 2000 + 8000 2 = 10000 2 = 5000 m/s . The time t taken to travel the distance s is given by t = s v_ avg . Substituting the values, t = 4 5000 = 4 5 10^3 = 0.8 10⁻³ s . Converting this to scientific notation, t = 8 10⁻⁴ s . Answer: 8 10⁻⁴ ~s