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
[tex]v(6)=\int_{0}^{4} 0.4545t \,dt = 0.22725 [t^{2}]_{0}^{4} = 3.636 \, m/s[/tex]
A graph of velocity versus time is shown.
Answer: 3.636 m/s
