(a) Newton third law of motion states that action and reaction are equal and opposite and they act on different bodies.
(b) Action and reaction act on different bodies.
(c) This is because the action and reaction forces always act on different bodies.
(d) When a shot is fired from the gun with some force in the forward direction, the shot in turn exerts an equal and opposite force on the gun, causing it to recoil or kick backwards.

Here  m = 500 g = 0.5 kg,  \(u = 50 \ ms^{-1},\)    v = 0,    t = 0.01 s
\(F = ma = m \left( \frac {u-v}{t}\right)=0.5\left(\frac{0-50}{0.01}\right)=-\frac {0.5 \times 50}{0.01}=-2,500 N\)
Magnitude of force of nail on hammer = 2,500 N.

Here,     m = 10 g = 0.01kg,  \(u = 1500 m s^{-1},\)  v = 0,  t = 0.03 s
 \(a = \frac {v-u}{t}=\frac {0-150}{0.0.3}=-5,000 m s^{-2}\)
The distance of penetration of the bullet into the block,
 \(s = ut + \frac {1}{2} at^{2}= 150 \times 0.03 + \frac {1}{2} \times (-5,000)\times (0.03)^{2}\)
 \(= 4.5 - 2.25 = 2.25 m.\)  

(i) Zero, because both are at rest.
(ii) Zero, in accordance with the law of conservation of momentum.

Let m bet the mass of the car.  Then \(=\frac { { F }_{ 1 } }{ { F }_{ 2 } } =\frac { { ma }_{ 1 } }{ { ma }_{ 2 } } =\frac { 1.8 }{ 1.2 } =\frac { 1.8 }{ 1.2 } =\frac { 3 }{ 2 } .\)
Therefore, the ratio is 3 : 2.

F = 400 N,   m = 8 kg,  \(u = 150 m s^{-1},\)   \(v = 300 ms^{-1}\)
Acceleration,   \(a=\frac { F }{ m } =\frac { 400 }{ 8 } =50\quad { ms }^{ -2 }\)
Time    \(t=\frac { v-u }{ a } =\frac { 300-150 }{ 50 } =3\quad s.\)

Here, F = 0.6 N,     \(u={ 5 }ms^{ -1 },\)   \(v=6{ ms }^{ -1 },\)   t = 2 s
Acceleration, \(a=\frac { u-v }{ t } =\frac { 6-5 }{ 1 } =\frac { 1 }{ 2 } { ms }^{ -2 }\)
Mass,   \(m=\frac { F }{ a } =\frac { 0.6 }{ 1/2 } =1.2\)

Here   u = 0,     v = 30 m/s,        t = 10 s
\(\therefore\)    \(a=\frac { u-v }{ t } =\frac { 30-0 }{ 10 } =3m/{ s }^{ 2 }\)
Now  m = 1500 kg,  \(a=3m/{ s }^{ 2 }\)
\(\therefore\)  Required force,   \(F=ma=1500\times 3N=4500N\)

First law of motion as a special case of second law. According to second law,
 \(F= ma = m \left(\frac{u-v}{t}\right)\)
\(Ft = m \left(u-v\right)\) 
That is when F = 0, v = u for whatever time t is taken because \(m \neq 0.\) This means that the object will continue moving with uniform velocity u throughout the time t. If u is zero then v will also be zero. That is the object will remain at rest. This is nothing but Newton's first law of motion. Hence first law of motion is contained in the second law.

Momentum. Momentum of a body is the quantity of motion possessed by the body. it is equal to the product of the mass and velocity of the body and is denoted by p.
\(Momentum = Mass \times Velocity\)
\(p = mv\)
Momentum is a vector quantity and its direction is the same as the direction of velocity of the object.

1. When a moving bus stops, the lower part of our body in contact with the bus comes to rest while the upper part of out body tends to keep moving due to inertia of motion. Hence, we fall downwards (or forwards).
2. When the bus accelerates from rest, the lower part of our body comes into motion along with the bus while the upper part of body tends to remain at rest due to inertia of rest. hence we fall backward.

A sudden movement of the vehicle results in the sudden change in the state of motion of the vehicle and of our feet in contact with it. But the rest of our body oppose this change due to its inertia and tends to remain where it was. Seat belts are provided to protect the passengers from falling backward or forward during such situations.

Inertia of Motion. The tendency of a body to remain in its state of uniform motion in a straight line, is called 'inertia of motion'.
Examples:
(i) An athlete runs for certain distance before taking a jump so that his inertia of motion may help him to take a longer jump.
(ii) if a horse running fast suddenly stops, the rider is thrown forward if he is not firmly seated.

Inertia of Direction. The inability of a body to change by itself its direction of motion is called 'inertia of direction'.
Examples:
(i) When a dog chases a hare, the hare runs along a zig-zag path. It becomes more difficult for the dog to catch hare because dog has more inertia of direction than that of the hare.
(ii) As a bicycle moves, the water drops sticking to its tire start leaving it tangentially.