If it takes total work W to give an object a speed v and kinetic energy K , starting from rest, what will be the object’s speed (in terms of v) and kinetic energy (in terms of K) if we do twice as much work on it, again starting from rest?

Solution 4DQ Step 1 of 4: In the given problem we need to calculate the velocity and kinetic energy when work is doubled. From work energy theorem, the work done is equal to change in kinetic energy. That is, W = KE W = KE fKE i Using KE= mv 1 2 W= mv1 2 - mv 2 2 2 f 2 i Initially the object is at rest, so the initial velocity will be i= 0, v W= mv1 2 2 f 1 2 Also KE=W= mv 2 f …………….1 Step 2 of 4: When total work is W to give an object a speed v and kinetic energy K , starting from rest. 1 2 That is, KE =1 = mv 1 2 1 ………….2 Solving for velocity, 2 2KE 1 v 1 = m 2KE 1 v 1 = m …………..3