Confirm correctness of simple Newton's second law-type problem?

[zero_infinity]

Homework Statement

at t=0, a 4kg mass is moving at 2 m/s\hat{i} + 3m/s\hat{j}
at t=0, F₁ and F₂ act upon the object
F₁= [1 N + (1/2 N/s)t ]\hat{i}
F₂= -(1/3 N/s²)t² \hat{j}

a) what is the object's velocity when t=3?
b) at what time does the object stop moving in \hat{j} direction?
c) what is the object's displacement when t=6?

Homework Equations

F=ma
kinematics

The Attempt at a Solution

just look at the steps and see if I'm doing it right please

\vec{V}₀ = 2 m/s\hat{i} + 3m/s\hat{j}
\vec{F}(t) = [1 N + (1/2 N/s)t ]\hat{i} - (1/3 N/s²)t² \hat{j}


(a)
\vec{F}(t) = m\vec{a}
\vec{F}(3)/4 kg = \vec{a}

Use \vec{V}_f = \vec{V}₀ + \vec{a}t

\vec{V}_f = 21/8 \hat{i} - 3/4 \hat{j}





(b)
just look at the \hat{j} component of the vector

\vec{F}_j(t)/ 4kg = \vec{a}_j
Use \vec{V}_f = \vec{V}₀ + \vec{a}t

0 = 3m/s\hat{j} - \vec{a}_jt

t = 3.30 s





(c)
\vec{F}(t)/ 4kg = \vec{a}(t)

actually, now when I'm rewriting it, I'm not sure how to integrate \vec{a}

do i integrate the acceleration from 0 to 6? i don't think so...

i integrated acceleration (not accounting for C) and then integrated velocity from 0 to 6 (this is obviously wrong now that I'm looking over it)

 

[rl.bhat]

Find the velocity and acceleration along i and j directions separately.
Using proper kinematic equations find the remaining answers by using vector addition.

 

[zero_infinity]

Find the velocity and acceleration along i and j directions separately.
Using proper kinematic equations find the remaining answers by using vector addition.

Hi

which part are you talking about?

 

[rl.bhat]

Voi = 2 m/s, F1i = 1N. Find a1i.
Similarly find Voj, F2j and a2J.
Calculate Vfi and Vfj after 3 s.