A car accelerates from rest of u m s - 1 . The energy spent in this process is E J . The energy required to accelerate the car from u m s - 1 to 2 u m s - 1 is n E J . The value of n is _____.

Step-by-step solution

The kinetic energy of a moving particle is given by E = 1 2 m u 2       . . . ( 1 ) When the final velocity of the particle becomes twice the initial velocity, the kinetic energy of the particle can be written as n E = 1 2 m ( 2 u ) 2 - u 2 =   1 2 m 3 u 2       . . . 2 Divide equation (2) by equation (1) and solve to calculate the value of n . n E E = 1 2 m 3 u 2 1 2 m u 2 ⇒ n = 3