I have a 2002 Odyssey EX, which has done 52K miles. Off late, when I press the accelerator, I notice a slight vibration and a hesitation in the car. It’s almost like the car takes time to respond to the acceleration request.
I’m a newbie when it comes to car maintenance. I’m wondering if this is related to the transmission and whether it will be an expensive proposition to fix.
It sounds like an engine performance problem. When, if ever, has the fuel filter been replaced?
What about the spark plugs? (Yes, I know spark plugs are allegedly good for eternity). 
Any Check Engine Light ever come on, drop off in fuel economy, or even a hint of a slightly rough idle?
Does it feel like driving over rumble strips?
I wish I could describe it better. When I accelerate, the car seems to lose some power, then it picks speed. Also, there is some vibration at that point - I guess yes, it would be kind of like driving over rumbling strips.
A friend said it may have to with the engine mount.
Still confused.
It sounds like an engine performance problem. When, if ever, has the fuel filter been replaced?
What about the spark plugs? (Yes, I know spark plugs are allegedly good for eternity).
Any Check Engine Light ever come on, drop off in fuel economy, or even a hint of a slightly rough idle?
The idle seems OK. And the engine light has not come on. I can definitely get the fuel filter and the spark plugs checked. Thanks.
It could be lot of things and it will take an experienced person to drive it and start figuring it out. I would start by checking the trans fluid. Is it full, pink and not dark and burned-smelling? After that, take it to an experienced mechanic.