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.