Answer
$v_{max}=18m/s$
Work Step by Step
Maximum speed is achieved when acceleration is equal to zero. Solving for when acceleration equals zero gets a time of $$0.0=6.1-1.2t$$ $$1.2t=6.1$$ $$t=5.1s$$ Note that velocity can be calculated from acceleration using the equation $$v(t)=\int a(t) dt + v_o$$ Using $v_o=2.7m/s$, substituting acceleration into the formula, and using power rule to integrate yields a velocity of $$v(t)=(6.1t-0.60t^2+2.7)m/s$$ Substituting this value of $t=5.1s$ into time yields a velocity of $$v(5.1)=(6.1(5.1s)-0.60(5.1s)^2+2.7)=18m/s$$
