Need help with gravity simulation in 2D game engine

I'm writing a 2D game engine using C++ and SDL2 and started implementing a rigidbody component similar to that of unity to my game objects. I have a method in the rigidbody class called AddForce which takes a 2D vector force as a parameter and calculates the velocity vector using \$F = MA\$.

I use this function to move the character left and right using the keyboard arrows. Now my question is, how do I manage the gravity with this and how do I calculate the resultant force of the gravity and the force applied when pressing either keyboard arrows.

Here is the rigidbody class:

#ifndef RIGIDBODY_H
#define RIGIDBODY_H

//Game engine libraries
#include "gameEngine/Game.h"
#include "gameEngine/GameObject.h"
#include "gameEngine/Component.h"
#include "gameEngine/components/Transform.h"

//GlM library
#include "glm/glm.hpp"

class RigidBody : public Component
{
private:
    Transform* m_transfrom;
private:
    float m_mass;
    float m_acceleration;
    glm::vec2 m_forceApplied;
    glm::vec2 m_velocity;
private:
    float m_deltaTime;

public:
    RigidBody(float mass)
    {
        m_name = "RigidBody";
        m_mass = mass;
        m_acceleration = 0;
        m_forceApplied = glm::vec2(0,0);
        m_velocity = glm::vec2(0,0);
     }
public:
     void AddForce(glm::vec2 force, float deltaTime)
     {   
        float forceMagnitude;
        m_deltaTime = deltaTime;
        m_forceApplied = force;

        forceMagnitude = glm::length(force);
        m_acceleration = forceMagnitude / m_mass;
      }    
 private:
     glm::vec2 CalculateVelocity()
     {
         float velocityMagnitude;
         static glm::vec2 newVelocity = glm::vec2(0,0);

         velocityMagnitude = m_acceleration * m_deltaTime;

         if(m_forceApplied.x != 0 || m_forceApplied.y != 0)
             newVelocity = glm::normalize(m_forceApplied);
         else
           newVelocity = glm::vec2(0,0);

         newVelocity = newVelocity * velocityMagnitude;

         return newVelocity;
      }

 public:
    void Initialize() override
    {
        m_transfrom = m_owner->GetComponent<Transform>("Transform");
    }
    void Update(Game instance, float deltaTime) override
    {
        m_velocity += CalculateVelocity();
        m_transfrom->position.x += m_velocity.x * deltaTime;
        m_transfrom->position.y += m_velocity.y * deltaTime;
    }
    void Render() override
    {

    }
 };

 #endif