I have 06 mini cooper s convertible with automatic transmission 40k miles.

I tried to record video for explaining more details but it happens randomly.

yesterday, i've been driving around 35-40 in local city and suddenly while i was stepping on brake, rpm bumps up to 7000 with wheel spin and car went forward without stepping on gas. my friend on passenger side and i were so shocked. this was not the first time. it's already been several times.
today, i drove on uphill road and it doesn't shift 3rd to 4th gear smoothly and it slips sometime when shifting down 2nd to 1st gear. I'm using paddle shifter if it doesn't shift even though rpm is over 5000. there was burning smell coming in to interior. all windows were closed.
is it because of transmission or engine? Please advise.

 

Confusing post , your saying while stopping it spins the tires accelerating? Or is it going into neutral no revving instead of downshifting ?

 

car was going around 35-40mph and tried to slow down little and stepped on brake little and it happened.

 

So the car sped up while stopping? Or did it just rev

 

first one. rpm was at 2500 and suddenly goes up to 6000-7000 rpm for few seconds and back to normal rpm.

 

If it's just revving that sounds like something with the downshift that would be transmission related if you had anything with the downshift engine related you would have a rough idle from the vacuum leak present