Final answer:
To increase the power output of a lawnmower, increasing the speed of push or adding more horsepower to the engine are effective methods; whereas improving blade size or decreasing fuel efficiency are not directly related to power. A lawnmower gains energy when pushed and loses it due to friction.
Step-by-step explanation:
In physics, power is the rate at which work is done, and it can be increased by various methods that affect how a lawnmower operates. Among the options provided, increasing the speed at which the lawnmower is pushed (option c) and adding more horsepower to the lawnmower engine (option d) are direct ways to increase the power output. Increasing the size of the lawnmower blades (option a) could potentially cover more ground in the same amount of time, but it is not directly related to power output. Decreasing fuel efficiency (option b) would not increase the lawnmower's power; it would likely lead to more fuel being consumed without necessarily increasing the rate of work done.
When a person does work on the lawnmower like pushing it, they are transferring energy to the mower. The mower would gain energy as the person applies a force to push it, and it would lose energy through friction with the grass and air resistance. The Work-Energy Theorem, expressed as W = Fd cos 0, where W is the work done, F is the force applied, d is the displacement of the mower, and 0 is the angle of the force, provides a quantitative measure of this energy transfer.