Your logic and your solution seem fine to me.

Perhaps you were surprised by the numerical size of the solution,

(perhaps expecting kilo-joules or similar magnitudes).

If we consider the definition of a Joule: <

wikipedia:joule>

Then one Joule is equal to the energy transferred to (or work done on) an object when a force of one Newton acts on that object in the direction of its motion through a distance of one metre.

If we give the object a mass of 1Kg then 1 Newton will accelerate it at 1 m/s/s.

from S=ut+1/2at^2 we can get the time taken for the object to travel 1 metre (accelerating at 1m/s/s from zero).

2=t^2 thus t=1.4142...

In other words 1 Joule will accelerate 1 Kg at 1m/s/s over a distance of 1 metre in just under one and a half seconds.

Looking at this analysis of the magnitude of a joule (with respect to our more familiar units) will hopefully reassure you that 20 joules is not an unreasonable solution.