Question

When a force of $1N$ acts on a mass of $1kg$ that is able to move freely, the object moves with a/an
$A.$ Speed of $1m{{s}^{-1}}$
$B.$ Acceleration of $1m{{s}^{-2}}$
$C.$ Speed of $1km{{s}^{-1}}$
$D.$Acceleration of $10m{{s}^{-2}}$

Answer 1

We will use the mathematical relation of Newton’s second law of motion to find the correct answer. Newton’s second law of motion states that the rate of change of linear momentum is directly proportional to the force applied and takes place in the direction of force applied. We also know that the force is the product of mass and acceleration.

Formula Used: We will use the following formula to get the correct answer:-
$F=ma$.

Complete step by step answer:
From Newton's second law of motion we know that the force $(F)$ is the product of mass $(m)$ and acceleration $(a)$.
i.e. $F=ma$…………… $(i)$
From the question we have force, $F=1N$ and mass, $m=1kg$ and we therefore have to calculate the acceleration.
From equation $(i)$ we get
$a=\dfrac{F}{m}$………………. $(ii)$
Putting values in $(ii)$, we get
$a=\dfrac{1N}{1kg}$
$\Rightarrow a=1N/kg$
∴$a=1m{{s}^{-2}}$

Hence, option $(B)$ is correct.

Additional Information:
We should have a brief idea about the acceleration, force and Newton’s second law of motion to have a better grip on these types of problems.
Acceleration is defined as the rate of change of velocity.
Force is defined as an external agent which changes the state of the body or tends to change the state of the body.
Newton’s second law of motion states that the rate of change of linear momentum is directly proportional to the force applied and takes place in the direction of force applied.
Mathematically, it is represented as $F=ma$.

Note:
Mathematical relation of force, mass and acceleration should be used correctly. We should take care of units properly. We should remember that Newton is a name given to the unit $kgm{{s}^{-2}}$. If we take care of these things then our answer will be correct most of the time.