A 4 kg mass moves under the influence of a force $\vec{F}$ = (4t³î - 3tĵ) N where t is the time in second.
If mass starts from origin at t = 0, the velocity and position after t = 2s will be :
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Question

A 4 kg mass moves under the influence of a force $\vec{F}$ = (4t³î - 3tĵ) N where t is the time in second.

If mass starts from origin at t = 0, the velocity and position after t = 2s will be :

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G1 Physics · Accepted Answer

The mass is m = 4 kg. Therefore, a⃗ = F⃗ ─── m . Hence the x-component of acceleration is aₓ = t³, and the y-component is a₍y₎ = - 3t ─── 4 . Following the supplied source solution, the initial velocity is taken to be zero. vₓ = ∫₀ᵗ t³ dt = t⁴ ─── 4 . At t = 2 s, vₓ = 4 m·s⁻¹. Also, v₍y₎ = ∫₀ᵗ - 3t ─── 4 dt = -3t² ──── 8 . At t = 2 s, v₍y₎ = - 3 ─── 2 m·s⁻¹. Thus, v⃗ = 4î - 3 ─── 2 ĵ. Now integrate the velocity components to obtain position. x = ∫₀ᵗ t⁴ ─── 4 dt = t⁵ ─── 20. At t = 2 s, x = 8 ──…

A 4 kg mass moves under the influence of a force F ⃗ \vec{F} F = (4t³î - 3tĵ) N where t is the time in second. If mass starts from origin at t = 0, the velocity and position after t = 2s will be :