A US car website managed about 6.5s 0-60. The European figures are 0-62 (100kph; about .2 difference or so for this car) and the official for the soft top is 7.6s, 7.9 is for the folding hard top which is 80kg heavier.
Seems like they are underselling the car, and it will beat this figure but if you look at an MX-5 purely on the acceleration it is not the right car for you. It is such fun to drive, far more than a supercar that you cannot drive near its limits without a driving ban.
An aftermarket turbocharger for this sets you back about £4500 installed, and takes it to around 250-300 bhp (your choice: power or longevity). The set-up was allegedly designed to allow for boost, both in the engine strength & cooling and in space in the engine bay.
That will sort out a few rivals.