Using Uno to control a 5V non addressable led strip

a link to the strip would help
a link to the adapter would help

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I would guess 12V strip, 20mA per led (12 x 0,02 x 30 = 7.2W). Are you sure it's 5V ?

for 2m you need 14.4W under 12V which is 1200mA (60 leds x 20mA) so seems you are within the specs of your adapter but without info, we are in the wild guess territory

if you plan to drive it from an Arduino, yes you need a way to turn it on and off a logic level MOSFET would do.