The force needed to accelerate an elevator upward at a rate of [tex]2 m / s^{2}[/tex] is 2000 N or 2 kN.
Explanation:
As per Newton's second law of motion, an object's acceleration is directly proportional to the external unbalanced force acting on it and inversely proportional to the mass of the object.
As the object given here is an elevator with mass 1000 kg and the acceleration is given as [tex]2 m / s^{2}[/tex], the force needed to accelerate it can be obtained by taking the product of mass and acceleration.
[tex]\text {Force}=\text {Mass} \times \text {Acceleration}[/tex]
[tex]\text { Force }=1000 \times 2=2000 \mathrm{N}=2 \text { kilo Newon }[/tex]
So 2000 N or 2 kN amount of force is needed to accelerate the elevator upward at a rate of [tex]2 m / s^{2}[/tex].
