Q: The car accelerates slowly, hesitates and shudders

My car started having some issue the other day, while I was driving and tried to accelerate very quickly. The car seemed to lose power and there was a delay in picking up speed. The engine hesitated and if I attempted to accelerate more, it would shudder. The problem is the same if the car idles at the red stop and I try to accelerate. I fear that it would stall, so in those situations I put it in park just in case. Occasionally, the engine seems to gather the speed quickly and but the car wouldn't run fine afterward. It would then hesitate and shudder yet again. The check engine light is on as well. The car shakes only when it is put in drive, not while I accelerate from neutral. I had the spark plugs replaced. What is causing these issues? Is it a serious engine problem?