Unity - character falling faster than jumping - unity3d

Question

I'm trying to implement my own gravity for a character.
But for some unknown to me reason the character's landing speed is higher landing than when jumping, by quite a lot (~15 initial jump speed, ~24 final land speed). I'm ultimately trying to replicate behavior shown on the gif below.
https://imgur.com/a/q77w5kS
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.AI;
public class Movement : MonoBehaviour {
public float speed = 3;
public float jumpSpeed = 15;
public float gravity = -1f;
private float ySpeed = 0;
private float jumpTime = 0;
private bool direction = false; //true for going up, false for falling down - gravity
private bool previousDirection = false; //to keep track of changing direction
private CharacterController _characterController;
// Start is called before the first frame update
void Start() {
_characterController = GetComponent<CharacterController>();
}
// Update is called once per frame
void Update() {
float dx = Input.GetAxis("Horizontal");
float dz = Input.GetAxis("Vertical");
float dy = Input.GetAxis("Jump");
// move around
Vector3 movement = new Vector3(dx, 0, dz);
// limit diagonal movement
movement = Vector3.ClampMagnitude(movement, 1);
// speed
movement *= speed;
// change of direction
if(ySpeed>0 && direction!=true)
direction = true;
else if(ySpeed<0 && direction!=false)
direction = false;
// if changed direction - peak of the jump
if(direction!=previousDirection){
Debug.Log("Jump Time = " + jumpTime);
jumpTime = Time.deltaTime;
previousDirection = direction;
}
// jump/on ground
if(_characterController.isGrounded) {
ySpeed = -0.5f;
jumpTime = 0;
if(dy > 0f){
ySpeed = jumpSpeed;
}
}
// gravity - when not on ground
else{
// dv/dt
ySpeed += gravity*jumpTime;
// add jump time
jumpTime += Time.deltaTime;
// Debug.Log(jumpTime);
Debug.Log(ySpeed);
}
movement.y = ySpeed;
// direction adjustment
movement = transform.TransformDirection(movement);
movement *= Time.deltaTime;
_characterController.Move(movement);
}
}

Answer 1

I think I figured out what was wrong with my idea.
ySpeed += gravity*jumpTime
So every frame I'm adding more and more acceleration downwards. This should just be: ySpeed += gravity *Time.deltaTime
(Acceleration due to gravity is then constant, not getting greater as time passes)
It is being integrated over many steps, so each Update() cycle is a slice of time that adds some velocity based on acceleration due to gravity, multiplied by the amount of time taken by that little slice.
In another words...
Gravity is a constant acceleration. I've made it a linear function of the time spent in the air. So, I start the jump with no gravity and end the jump with very high gravity.