Question

Give the relation between acceleration, mass, and force.

Answer 1

Step1: Newton's second law

1. Newton's second law describes the relationship between the three quantities above.
2. The rate of change of momentum of a body is equal to the force exerted on the body in a given direction, according to Newton's second law of motion.

Step2: Formula used

Consider a body with mass $\text{'}m\text{'}$ that moves at velocity $\text{'}v\text{'}$. As a result, the body's momentum $\text{'}p\text{'}$ is given by,

$p=mv$

Step3: Relation between acceleration, mass, and force

We now know that the rate of change in momentum of a body is equal to the force applied to the body thanks to Newton's second law of motion. As a result, the force $F$ equals, $F=\frac{dp}{dt}=\frac{d\left(mv\right)}{dt}[Asp=mv]$

$F=v\frac{dm}{dt}+m\frac{dv}{dt}...........equtaion\left(i\right)$

The acceleration $\text{'}a\text{'}$of a body is defined as the rate of change of velocity i.e. $\frac{dv}{dt}$

since mass does not change with time equation $\left(i\right)$ can be written as,

$$\begin{gathered} F=v\frac{dm}{dt}+m\frac{dv}{dt} \\ F=v\left(0\right)+ma \\ F=ma \end{gathered}$$

Hence the required relation between acceleration, mass, and force is given by $F=ma$