Find the speed of the particle?

Question

Find the speed of the particle with position function r(t)=e^3t i+e^-3t j+te^3t k when t=0.

Answer 1

Speed is the magnitude of the velocity function

so first we need to find v(t) = r ' (t)

r ' (t) = 3e^3t i - 3e^-3t j + (3te^3t + e^3t)k

so v(0) = r ' (0) = 3e^0 i -  3^0 j + (3*0e^0 + 3^0)k = 3i - 3j + k

so then magnitude of velocity at t = 0 is sqrt(3^2 + (-3)^2 + 1^2) = sqrt(9+9+1) = sqrt19