A net force acts on an object and accelerates it from rest to a speed v1. In doing so, the force does an amount of work W1. By what factor must the work done on the object be increased to produce three times the final speed, with the object again starting from rest?

Solution 13DQ Introduction The work done by the force on the object will be equal to the work done kinetic energy gained by the object during its acceleration. Now since the object started from rest, the final kinetic energy of the object will be equal to the work done by the force. Hence we will calculate the final kinetic energy and compare the work done. Step 1 Suppose m is the mass of the object. Hence the kinetic energy after achieving the velocity v1is 1 2 E k1 = 2v 1 Since, all the energy of gained by the object coming from the force applied to the object, from the conservation of energy we can say that the kinetic energy gained by the object is equal to the work done by the force. Hence we have E k1 = W 1 mv2 12