The kinetic energy of an object with a mass of #1 kg# constantly changes from #243 J# to #658 J# over #9 s#. What is the impulse on the object at #3 s#?
You must aknowledge that the key words are "constantly changes". Afterwards, use the kinetic energy and impulse definitions.
The impulse is equal to the change of momentum:
However, we are missing the velocities.
Constantly changing means that it changes "steadily". This way, we can assume that the rate of change of the kinetic energy
So for every second the object gains
Therefore the kinetic energy at
Now that both kinetic energies are known, their velocities can be found:
Finally, the impulse can be calculated: