Gear not shifting instantly?

I own a 2009 Honda Accord Coupe V6.

I drive my brothers and my sisters car as well. I noticed a difference between my car and theirs. When I shift from Park to Drive, my car doesn't instantly start moving (it takes about a second for the car to move). But in my brothers Ford Mondeo and my sisters Ford Focus, it instantly starts moving. My car takes about a second as I said, and the same thing goes if I shift from Neutral to Drive. It also feels like the car jumps suddenly (like a sudden bump?) I don't really know how to explain this. Is this natural? What could be causing this?

What are we talking about? A "lag" of a second or two - - - or that you have to sit there for 30 seconds, a minute or longer waiting for the gears to engage?

US cars have for some years had an interlock that prevents engaging Drive or Reverse without the brake pedal being firmly depressed. That's a safety feature, but also saves wear on the transmission: gear range should be fully engaged before releasing the brakes - - - and nothing is harder on the trans than throwing it into Drive while gliding to a stop in Reverse (or vice versa). If you want it to last, never change ranges unless the car is at a dead standstill.

But, if it takes more than a second or two for the gears to engage - that's a sign of worn clutches, or low fluid pressure from bad seals or failing pumps. Nurse it - it won't get better.

Check tranny fluid level