I need help with these. Please show workings

Answer:
Imp = 25 [kg*m/s]
v₂= 20 [m/s]
Explanation:
In order to solve these problems, we must use the principle of conservation of linear momentum or momentum.
1)
[tex](m_{1}*v_{1})+(F*t)=(m_{1}*v_{2})[/tex]
where:
m₁ = mass of the object = 5 [kg]
v₁ = initial velocity = 0 (initially at rest)
F = force = 5 [N]
t = time = 5 [s]
v₂ = velocity after the momentum [m/s]
[tex](5*0) +(5*5) = (m_{1}*v_{2}) = Imp\\Imp = 25 [kg*m/s][/tex]
2)
[tex](m_{1}*v_{1})+(F*t)=(m_{1}*v_{2})\\(0.075*0)+(30*0.05)=(0.075*v_{2})\\v_{2}=20 [m/s][/tex]
Force = F = 5N
time = t = 5 seconds
mass = m = 5 kg
momentum = p = ?
The force which acts for a very short period of time is called impulse force. It is given by,
I = F x t
Where,
I is impulse
F is force
t is time till which force is exerted
The impulse experienced by the object equals the change in momentum of the object. In equation form,
F x t = M x ΔV
So,
F x t = Final momentum - initial momentum
F x t = final momentum - (0)
initial momentum is zero because the object was initially at rest.
Final momentum = 5 x 5
Final momentum = 25 [tex]kgms^{-1}[/tex]
So B is the answer
Force = F = 30 N
time = t = 0.05 seconds
mass = m = 0.075 kg
V = ?
impulse force is given by,
I = F x t
Where,
I is impulse
F is force
t is time till which force is exerted
The impulse experienced by the object equals the change in momentum of the object. So,
F x t = M x ΔV
So,
F x t = Final momentum - initial momentum
F x t = final momentum - (0)
Since it was at rest initially, initial momentum is zero.
Momentum is given by,
p = m x V
where,
p is momentum
m is mass
v is velocity
F x t = m x V
Rearrange the equation,
V = [tex]\frac{Fxt}{m}[/tex]
[tex]V = \frac{(30)x(0.05)}{0.075} \\\\V = 20 m/s[/tex]
So C is the answer