Constitution

Read the following fact pattern.  Was this an allowable stop?  Was this an allowable search and arrest.
On March 17, 2016, Police Officer Smith, of the Street Crime Unit, Mobile Taxi Homicide Task Force, was on motor patrol in a marked police car in Manhattan, NY.  Their main assignment was to follow taxi cabs to make sure no robberies occurred. 
As the officer was driving north on Broadway, he observed a southbound car, traveling at a high rate of speed, pass a red light at the intersection. Seeing that the vehicle was a big four-door car, Officer Smith, although not a hundred percent sure, assumed it was a livery cab. While Smith could see the driver, he could not determine whether there were any other occupants. Smith turned the police vehicle around, and the officer activated the high density lights and pulled the cab over. Smith did not intend to issue a summons but, instead, planned to give the driver a leaflet on safety tips and instruct him. As the cab pulled over, with the police vehicle directly behind, Smith observed defendant, seated in the cab’s rear compartment, turning two or three times to view the officer.
Smith exited the police vehicle and approached the cab on the passenger side.  Smith held a flashlight but had not drawn his gun. Smith shined his flashlight into the back of the cab where defendant was seated, wearing a leather jacket that was about three-quarters closed, with the top part open so that Smith could see defendant’s shirt. Noticing a puffy area around defendant’s chest that was bulging out, Smith believed that defendant was wearing a bulletproof vest. When, at Smith’s request, defendant stepped out of the car, Smith placed his hand on defendant’s chest where the jacket was open and confirmed his suspicion of a bulletproof vest.
Then Smith, without leaning into the car, shined his flashlight through the open door into the passenger compartment and saw a small revolver on the floor, right in front of where defendant had been seated. Smith handcuffed defendant and recovered the gun, which contained five rounds of ammunition. The defendant stated, It’s not my gun.