A rocket’s thrust is modeled by

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

T(t)=m(t)v(t)

, where

m(t)

is the mass flow rate of exhaust (kg/s) and

v(t)

is the exhaust velocity (m/s). At

t=3\text{ s}

, measurements give

m(3)=2,\;m'(3)=0.10,\;v(3)=5,

and

v'(3)=0.40

. Determine

T'(3)

, the instantaneous rate of change of thrust, in newtons per second.