Chapter 12 - Practice Exercises - Page 674: 22

$a(0)=2 \sqrt 2T +2 \sqrt 3N$

$v(t)=\dfrac{dr}{dt}=1 \ i +(1+4t) \ j +2 \ t \ k$ $a(t)=\dfrac{dv(t)}{dt}=4 j +2k$ $\implies |a(t)|=\sqrt {4^2+(2)^2} \implies |a(t)|=2 \sqrt 5$ Now $a_{T}(0)=2 \ \sqrt 2$ $a_{N}=\sqrt {|a(0)|^2 -a^2_{T} (0)}\\=\sqrt {(2 \sqrt {5})^2 -(2 \sqrt 2)^2} \\=2 \sqrt 3$ and $a(0)=a_T(0) T+a_{N} N \\ =2 \sqrt 2 \ T +2 \sqrt 3 \ N$