Since similar questions pop up in PPRuNe from time to time, it may be useful to recall that two requirements govern turbine engine acceleration times. The first is for the uninstalled engine, the second for the engine installed in the airplane, supplying bleed air and power for aircraft services:
Part 33 AIRWORTHINESS STANDARDS: AIRCRAFT ENGINES
Subpart E--Design and Construction; Turbine Aircraft Engines
Sec. 33.73 Power or thrust response.
[The design and construction of the engine must enable an increase--
(a) (...)
(b) From the fixed minimum flight idle power lever position when provided, or if not provided, from not more than 15 percent of the rated takeoff power or thrust available to 95 percent rated takeoff power or thrust in not over 5 seconds. The 5-second power or thrust response must occur from a stabilized static condition using only the bleed air and accessories loads necessary to run the engine. This takeoff rating is specified by the applicant and need not include thrust augmentation.]
Part 25 AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES
Subpart B--Flight
Performance
Sec. 25.119 Landing climb: All-engines-operating.
[In the landing configuration, the steady gradient of climb may not be less than 3.2 percent, with the engines at the power or thrust that is available 8 seconds after initiation of movement of the power or thrust controls from the minimum flight idle to the go-around power or thrust setting--
(a) In non-icing conditions, with a climb speed of VREF determined in accordance with Sec. 25.125(b)(2)(i); and
(b) In icing conditions with the landing ice accretion defined in appendix C, and with a climb speed of VREF determined in accordance with Sec. 25.125(b)(2)(ii).]