Question

What is the instantaneous velocity of an object moving in accordance to `f(t)=(12t,t^3)` at `t=1`?

Answer 1

Magnitude ( speed ) = `sqrt153` distance unit / time unit.
Direction> `psi = tan^-1 (1/4)` = 14.04 deg, nearly, from the x-axis.

Explanation:

Speed = `sqrt( (dx/dt)^2 + (dy/dt)^2) = sqrt( 12^2 + (3t^2)^2) = sqrt153`, at t = 1.

Direction: #tan^-1 (dy/dx) = tan^-1 (dy/dt/dx/dt) = tan^-1(t^2 / 4) = tan^-1(1/4)#, at t= 1..