a. The total mechanical energy, E (joules) of a particle partly varies as the potential energy, P (joules) and partly as the square of a speed, V (m/s) of the particle. A particle moving with a speed of 8 m/s when its potential energy is 125 joules has a total mechanical energy of 253 joules and when the speed is 6 m/s with potential energy 250 joules the total mechanical energy increased to 322 joules. Find
i. The relation between E, P and V
ii. The speed of the particle when its potential energy is 150 joules and its total mechanical energy is 350 joules.