People drive faster when they have auto insurance. This example illustrates

1. adverse selection.
2. asymmetric information.
3. moral hazard.

People drive faster after getting auto insurance is a problem of moral hazard. Moral hazard refers to the problem of asymmetric information that results in a cost for one party due to the other party's actions that occur after a contract/agreement or market exchange.

People know any accidents that could damage the vehicle will be covered by the insurance company, and therefore, they can choose to drive faster. The outcome of the bad decisions will put a cost on the insurance company that they did not know when selling the insurance.

Adverse selection is the problem of lemons. This happens when one party is unaware of certain information about the other party before entering into a contract or market exchange. This leads to a selection of bad goods or services, which are referred to as lemons. Since driving faster happens after buying auto insurance, this is not a part of the adverse selection problem.

Asymmetric information problems can result in both adverse selection and moral hazard depending on the reason and time of generation of cost for one party due to another party. Moral hazard is a more precise answer.