To solve the problem it is necessary to apply the Torque equations and their respective definitions.
The Torque is defined as,
[tex]\tau = I \alpha[/tex]
Where,
I=Inertial Moment
[tex]\alpha =[/tex] Angular acceleration
Also Torque with linear equation is defined as,
[tex]\tau = F*d[/tex]
Where,
F = Force
d= distance
Our dates are given as,
R = 30 cm = 0.3m
m = 1.5 kg
F = 20 N
r = 4.0 cm = 0.04 m
t = 4.0s
Therefore matching two equation we have that,
[tex]d*F = I\alpha[/tex]
For a wheel the moment inertia is defined as,
I= mR2, replacing we have
[tex]d*F= \frac{mR^2a}{R}[/tex]
[tex]d*F= mRa[/tex]
[tex]a = \frac{rF}{ mR}[/tex]
[tex]a = \frac{0.04*20}{1.5*0.3}[/tex]
[tex]a=1.77 m/s^2[/tex]
Then the velocity of the wheel is
[tex]V = a *t \\V=1.77*4 \\V=7.11 m/s[/tex]
Therefore the correct answer is D.
