Asituation were you can accelerate even though your speed doesn't change

'Acceleration' doesn't mean 'speeding up'. It means any change in the speed or direction of motion.  Any motion that's not constant speed in a straight line is accelerated motion.
Here are a few.  I'm sure you can think of lots more.

-- go around a curve on a bicycle or in a car
-- jump up in the air and come down again
-- jump from a diving board
-- stop pedaling or turn off the engine and coast to a stop
-- ride a satellite in orbit around the Earth
-- stand still on the Earth, and let it spin you around in a circle in 24 hours

Inner peace.. jk it's  a stable electron configuration