Question

An object moves with an initial velocity
vi = 3.30j m/s
and an acceleration
a = 2.60i m/s2.
Assume the object is initially at the origin.
(a) What is the position vector of the object as a function of time? (Express your answer in vector form. Use the following as necessary: t.)
r(t) =
m

(b) What is the velocity vector of the object as a function of time? (Express your answer in vector form. Use the following as necessary: t.)
v(t) =
m/s

(c) What is the position of the object at time
t = 3.50 s? (Express your answer in vector form.)
r(3.50 s) =
m

(d) What is the speed of the object at time
t = 3.50 s?

m/s

Answer 1

a(t) = 2.60 i
v(t) = ∫a dt + vi = 2.60t i + 3.30 j
r(t) = ∫v dt + 0 = 1.3t^2 i + 3.30t j
now finish it off, noting for (d) that the speed = |v|

Answer 2

Vi = 3.30 j
there is NO acceleration in the y direction so this is the y velocity forever.
therefore y = 3.30 t

A = 2.60 i
so
Vx = 2.60 t
x = 1.30 t^2/2 = 0.65 t^2

so
a = 2.60 i + 0 j
v = 2.60 t i + 3.30 j
position = 0.65 t^2 i + 3.30 t j

Answer 3

whoops 2.60 / 2 = 1.30 not 0.65