To avoid physically extracting secrets from the storage of devices, Physical Unclonable Function (PUF) is used in various authentication schemes. In these schemes, after the devices are registered on the Trusted Authority (TA), the subsequent authentication still must need the help of the TA. And these devices usually don't move. Due to the high mobility of vehicles, frequent involvement with the TA becomes expensive and impractical in motion. As a result, these schemes are not well suited to VANETs where devices move at high speeds. Motivated from this, we propose a physically secure and conditional-privacy authenticated key agreement scheme for VANETs. In the proposed scheme, PUF is utilized to prevent the physical extraction of secrets from vehicles and RSUs. Unlike others using PUF, the proposed scheme does not require the TA's participation during the authentication between the vehicles and RSUs. Meanwhile, the proposed scheme provides conditional-privacy with pseudonym mechanism, which enables the anonymity of legitimate vehicles and the tracking of malicious vehicles. Then, formal and informal security analysis show that the proposed scheme meets the expected goals and is secure against several known attacks in VANETs. Finally, compared with relevant studies, the proposed scheme has certain advantages in computation burden and communication burden.