Using second law of motion, derive the relation between force and acceleration.

In a two body collision, the momentum is varying with time as shown in graph. The instantaneous force is maximum at: 

The variation in momentum with time, for a body under collision is shown in figure. The maximum & minimum instantaneous forces are respectively on these points:

Read the following statements and choose the correct option:
Statement: Newton's second law of motion gives the measurement of force. 
Reason: According to Newton's second law of motion, force is directly proportional to the rate of change of momentum. 

A force ‘F’ is applied on one end of a rope of length ‘a’. P and Q are two points of length ‘b’ from nearest end. The ratio of tensions in string at P & Q is :

The velocity-time graph of a ball of mass $20 \mathrm{g}$ moving along a straight line on a long table is given in figure.The force exerted by the table on the ball to bring it to rest is :

A particle of mass $0.3 \mathrm{kg}$ is subjected to a force $F = Kx$with $K = 15 \mathrm{N}/\mathrm{m}$, what will be its acceleration if it is released from a point $x = 20 \mathrm{cm}.$

Two similar trucks are moving with the same velocity on a road. One of them is loaded while the other is empty. Which of the two will require a larger force to stop it?

A dynamometer D is attached to two masses $m_1=3 \mathrm{kg}$ and $m_2=5 \mathrm{kg}$. Forces of $f_1=9 \mathrm{N}$ and $f_2=25 \mathrm{N}$ are applied to the masses as shown.

The dynamometer will read :

What force is required to produce an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$ a body of mass $10 \mathrm{kg}$?

What is the direction of acceleration?

Define one newton.