What uniform force is required to accelerate a car weighing $100\,kgf$ from rest to $20\,m.{s^{ - 1}}$ while covering a distance of $20\,m$ ?
A. $1000\,N$
B. $100\,N$
C. $10\,kN$
D. $2000\,N$

Hint: In order to answer this question, first we will rewrite the given facts that are given in the question, and then we will first apply the formula in terms of both the velocities, acceleration and the distance to find the acceleration. Now, we have both acceleration and mass, so we can easily find the uniform force of the car, according to Newton's second law of motion.

Complete step by step answer:
At first the car is in rest position,
So, the initial velocity of the car, $u = 0\,m.{s^{ - 1}}$.
And, the final velocity is given, $v = 20\,m.{s^{ - 1}}$.
And the distance covered by the car, $s = 20\,m$.
So, to find the uniform force, we need to find the acceleration of the car:- we will apply the formula in terms of both the velocities, acceleration and the distance, i.e..-
${v^2} = {u^2} + 2as \\
\Rightarrow {20^2} = {0^2} + 2 \times a \times 20 \\
\Rightarrow 400 = 40a \\
\Rightarrow a = \dfrac{{400}}{{40}} = 10m.{s^{ - 2}} $
So, the acceleration of the car is $10m.{s^{ - 2}}$ .

Now, we have the mass of a car, $m = 100\,kgf$. Therefore, to find the uniform force to accelerate a car weighing $100\,kgf$ from rest to $20\,m.{s^{ - 1}}$ while covering a distance of $20\,m$ , we will apply the formula of the force in terms of mass and acceleration:-
$F = m.a \\
\Rightarrow F = 100 \times 10 \\
\therefore F = 1000\,N $
Therefore, the required force is $1000\,N$.

Hence, the correct option is A.

Note: The energy of a moving object is turned into work upon an impact, and force plays a significant role. Set the equations for energy and work equal to each other and solve for force to create an equation for the force of any impact.