How much force is needed to have a 50 kg object accelerate at a rate of 5 m/s²?

 (13.89 - 5.56) m/s /30 s = 8.33 / 30 = 0.278 m/s^2 

F = MA 
F = 150 kg * 0.278 = 41.65 N  

#2) Newton's Equations of motion 

distance = 0.5 * acceleration * time^2 + original velocity * time 
velocity = acceleration * time + original velocity 

First we need acceleration 

F = MA 
7 N = 0.4 kg*A (NOTE: I converted to consistent units: kg, m, s) 
A = 7/.4 = 17,5 m/s^2 

V = at + Vo 
80 m/s = 17.5 /s^2 * t + 0 (Started at rest) 

80 = 17.5 t 
t = 4.57 s 

#3 

First we need the weight of the book on the floor 

F = MA (A = 9.8 m/s^2 the acceleration of gravity) 
F = 0.4 kg * 9.8 m/s^2 = 3.92 N 

Now we need the Net Force on the book slowing it down (A = - 1.5 m/s^2) 

F = MA 
F = 0.4 kg * 1.5 m/s^2 = 0.6 N 

===> Friction is 0.6 N greater than your push or 5.6 N 

Weird!!! That means friction is greater than the weight of the book 

Mu (coff of friction) = Friction Force/Weight = 5.6 / 3.92 = 1,43 ( Nonsense answer) 

#4 We can do as a ratio 

70/400 = 1500/x 
70 x = 600,000 
x = 8,571 N