Find the velocity, acceleration, and speed of a particle with the given position function. r (t = t2i 6tj 4 ln t k

1st derivative gives velocity;

d r (t) / dt = 2t i + 6 j + 4/t k

2nd derivative gives acceleration;

d^2 r (t) / dt^2 = 2 i - 4 / t^2

Speed;

Square root of (4 t^2 + 36 + 16 / t^2)

For a given time, like 2 seconds, t will be 2. And answer of speed will be scalar.