A 5.50 kg object initially at rest at the origin is subjected to the time-varying force shown in the figure. What is the object'
s velocity at t=6s?
https://session.masteringphysics.com/problemAsset/2308967/2/knight_Figure_05_25.jpg
https://session.masteringphysics.com/problemAsset/2308967/2/knight_Figure_05_25.jpg
1 answer:
Refer to the figure shown below.
m = 5.50 kg, the mass of the object
The force is modeled by the piecewise function
F(t) = 2.5t N, 0 ≤ t ≤ 4 s
= 0, 4 < t ≤ 6 s
The acceleration due to the piecewise force is
a(t) = F(t)/m
That is,
a(t) = 2.5t/5.5 m/s², 0 ≤ t ≤4 s
= 0, 4 < t ≤ 6 s
The velocity at t = 6 s is
![v(6)=\int_{0}^{4} 0.4545t \,dt = 0.22725 [t^{2}]_{0}^{4} = 3.636 \, m/s](https://tex.z-dn.net/?f=v%286%29%3D%5Cint_%7B0%7D%5E%7B4%7D%200.4545t%20%5C%2Cdt%20%3D%200.22725%20%5Bt%5E%7B2%7D%5D_%7B0%7D%5E%7B4%7D%20%3D%203.636%20%5C%2C%20m%2Fs)
A graph of velocity versus time is shown.
Answer: 3.636 m/s
m = 5.50 kg, the mass of the object
The force is modeled by the piecewise function
F(t) = 2.5t N, 0 ≤ t ≤ 4 s
= 0, 4 < t ≤ 6 s
The acceleration due to the piecewise force is
a(t) = F(t)/m
That is,
a(t) = 2.5t/5.5 m/s², 0 ≤ t ≤4 s
= 0, 4 < t ≤ 6 s
The velocity at t = 6 s is
A graph of velocity versus time is shown.
Answer: 3.636 m/s
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Hope this helps!! :)