Question
State and explain Newton’s second law of motion.
✓
Answer
According to Newton's second law of motion: The rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction in which the force acts. Consider a body of mass $m$ having initial velocity $u.$ the initial momentum of this body will be $mu$. Suppose a force $F$ acts on this body for time $t$ causing the final velocity to be $v.$ The final momentum of the body will be $mv.$ Now the change in momentum is $mv → mu$ and the time taken for this change is t. So according to Newton's second law of motion, $\text{F}\propto\frac{\text{mv}-\text{mu}}{\text{t}}$ $\text{F}\propto\frac{\text{m}(\text{v}-\text{u})}{\text{t}}$ But $\frac{(\text{v}-\text{u})}{\text{t}}$ represents change in velocity with time i.e. ascceleration 'a'. So br replacing $\frac{(\text{v}-\text{u})}{\text{t}}$ with a in the above relation, we get $\text{F}\propto\text{m}\times\text{a}$ Thus, the force acting on a body is directly proportional to the product of mass and acceleration produced in the body by the action of the force. Thus, Newton's second law gives the relationship between force and acceleration.
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