A Rotorua mother and her teen daughter say they are grateful to be alive after a stolen car failed to stop at an intersection and collided at speed into the side of their vehicle.

The driver of the Mazda Demio and passenger ran away, leaving the woman and her daughter suffering injuries.

Police have confirmed a youth, who was the passenger in the Mazda, has been apprehended, but they are still looking for the driver.

The woman, who did not want to be named, says both vehicles are written off.

In response to Rotorua Daily Post questions, police say a silver Mazda Demio was stolen from outside a Mangakakahi house about 15 minutes before it crashed into the woman’s Toyota Hilux in Sunset Rd at 4pm on Monday last week.

The woman tells the Rotorua Daily Post the stolen car struck the driver’s side of the Hilux and shunted the Hilux into a pole that had a security camera on it, opposite the intersection with Ford Rd.

She was initially treated for neck injuries and both were taken to Waikato Hospital.

Both have been released from hospital, but have extensive seatbelt-related bruising. She says there's still pain in her elbow, but she's grateful the seatbelts saved them from being thrown from the vehicle.

“When the airbags go off they produce a lot of powder and at first, I thought it was smoke and the car was on fire. I was panicking because I couldn’t find [her daughter] because she had jumped out of the car.”

“We are okay, but it just makes you aware that things can change very quickly and unexpectedly. It’s made me grateful for having each day.”

-Rotorua Daily Post.