Starting at ttt_1 = 0 ss , a horizontal net force F⃗ =(F→=( 0.265 N/sN/s )ti^+)ti^+(-0.460 N/s2N/s2 )t2j^)t2j^ is applied to a box that has an initial momentum p⃗ =p→= (( -3.00 kg⋅m/skg⋅m/s )i^+()i^+( 4.05 kg⋅m/skg⋅m/s )j^)j^ .

The momentum of the box at t = 2 s is given as

p₂ = (-2.47î + 2.82ĵ) kgm/s

Explanation:

F = [(0.265 N/s)t] î + [(-0.460 N/s²)t²] ĵ

F = (0.265t) î - (0.460t²) ĵ

At t = 0

Initial momentum

p₀ = (-3.00 kg⋅m/s )î + (4.05 kg⋅m/s) ĵ

Find the momentum at t = 2 s

According to Newton's second law of motion, the change in momentum is equal to the impulse.

That is,

dp = F.dt

Δp = ∫²₀ F.dt

∫²₀ F.dt = ∫²₀ [(0.265t) î - (0.460t²) ĵ] dt

= [(0.1325t²) î - (0.1533t³) ĵ]²₀

= [0.1325(2²)] î - [0.1533(2³)] ĵ

∫²₀ F.dt= (0.53 î - 1.2267 ĵ) kgm/s

p₂ - p₀ = Δp = ∫²₀ F.dt = (0.53 î - 1.2267 ĵ)

p₂ = p₀ + Δp

p₂ = (-3.00î + 4.05ĵ) + (0.53 î - 1.2267 ĵ)

p₂ = (-2.47î + 2.8233ĵ) kgm/s

p₂ = (-2.47î + 2.82ĵ) kgm/s

Hope this Helps!!!

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two years ago, when picking flowers in the mountains back of yosemite valley, i found a book. it was blotted and storm-beaten; all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however; many of the inner pages were well preserved. and although all were more or less stained and torn, whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today; its granite pages have been torn and blurred by the same storms that wasted the castaway book.

two years ago, when picking flowers in the mountains back of yosemite valley; i found a book. it was blotted and storm-beaten, all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however, many of the inner pages were well preserved. and although all were more or less stained and torn; whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today, its granite pages have been torn and blurred by the same storms that wasted the castaway book.