The Girl Who Leapt Through Time

At Kuranose High School in Tokyo, Japan, Makoto Konno discovers a message written on a blackboard and inadvertently falls upon a walnut-shaped object. On her way home, Makoto is ejected into a railroad crossing when the brakes on her bicycle fail and is hit by an oncoming train, but finds herself transported back to the point in time when she was riding her bicycle right before the accident. After entering the Tokyo National Museum to meet with Kazuko Yoshiyama, she explains to Makoto that she has the power to "time-leap", to literally leap through time. At first, Makoto uses her powers to avoid being late, getting perfect grades, and even relive a single karaoke session for several hours, but soon discovers that her actions can adversely affect others. Read more on Wikipedia.