赴(おもむ)くto go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey

警察官(けいさつかん)が事件(じけん)現場(げんば)に赴(おもむ)いています。

The police officer is proceeding toward the scene of the incident. {to go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey}

子供(こども)たちは心(こころ)が赴(おもむ)くままに行動(こうどう)するべきだ。

Children should act according to where their heart leads them. {to go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey}

首相(しゅしょう)の最悪(さいあく)な政治(せいじ)のせいで国(くに)は破滅(はめつ)に赴(おもむ)いています。

Due to the Prime Minister's worst political policies, the country is heading towards ruin. {to go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey}

救援(きゅうえん)に赴(おもむ)く消防(しょうぼう)隊(たい)はまるで映画(えいが)の中(なか)のスーパーヒーローのようだ。

The firefighters heading to the rescue are like superheroes in a movie. {to go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey}

病気(びょうき)が快方(かいほう)に赴(おもむ)いているとあって、医師(いし)も看護(かんご)師(し)もホッとしているようです。

Given that the patient's condition is proceeding toward recovery, it seems that both the doctor and the nurse are relieved. {to go in the direction of, to proceed toward, to proceed according to, to repair to, to betake oneself to, to become, to face (facts, circumstances, etc.), to abide by, to agree to, to consent to, to obey}