Question

A glider is initially moving at a constant height of
3.62 m.
It is suddenly subject to a wind such that its velocity at a later time t can be described by the equation
v(t) = 16.12i − 7.84(1 + t)j + 0.80t3k,
where
v
and its components are in meters per second, t is in seconds, and the z axis is perpendicular to the level ground.
(a) What was the initial velocity of the glider? (Express your answer in vector form.)

In this one I know the answer is 17.93 (correct me if I'm wrong with the answer and an explanation) but its asking me to express it in vector form and I don't know how .

(b) Write an expression for the acceleration of the glider in component form when
t = 2.18 s.
(Express your answer in vector form.)
a(t = 2.18 s)
= m/s2

Answer 1

(a) v(t) = 16.12i − 7.84(1 + t)j + 0.80t3k
so, v(0) = 16.12i - 7.84j + 0k
That is certainly not 17.93, which is the speed

a(t) = dv/dt = 0i - 7.84j + 2.40t^2 k
so plug in t=2.18