If I set my speed at 40 mph with adaptive cruise control and approaching a fully stopped car in front of me, will the adaptive cruise control slow the car down gradually or the front emergency brake warn me and press the brake at the last second?

I was using cruise control yesterday on my local street at 40 mph and approaching a fully stopped car at red light. I thought my car would slow down just like using it on the highway. But it did not detect front car in a close range (there was no car icon ahead on the instrument panel). I had to brake it by myself. I did not test it closer to get front emergency brake triggered.