Answer:
The velocity of the block is 231650.8 ft/s
Explanation:
Knowing
W = 10 lb
v0 = u = 4 ft/s
F = 8 [tex]t^{2}[/tex] lb
ms = 0.2
Applying the newton second law
ΣFy = 0
N - W = 0 --> N = W = 10 lb
ΣFx = m[tex]a_{x}[/tex]
F - ms N = ma
[tex]8t^{2}[/tex]- 0.2(10) = [tex]\frac{10}{32.2} a[/tex]
a = [tex]3.22 (8t^{2} - 2)[/tex]
Using Kinematics
a = dv/dt
[tex]\int\limits^v_u dv[/tex] = [tex]\int\limits^t_0 {a} \, dt[/tex] = [tex]\int\limits^t_o {3.22 (8t^{2} - 2)} \, dt[/tex]
v - 4 = 3.22 [tex](\frac{8}{2} t^{3} - 2t)[/tex]
when t = 30
v = 231650.8 ft/s
