Question

Evaluate

d^2r/dt^2 at t=0 when

r=(t3+2t)i−3e−2tj+2sin5tk

Answer 1

$r=(t^3+2t)i−(3e+2t)j+2sin(5t)k\\ \frac{dr}{dt}=(3t^2+2)i-2j+10cos(5t)k\\ \frac{d^2r}{dt^2}=(6t)i-0j-50sin(5t)k\\ =6ti-50sin(5t)k$