how to detect sudden change in a sensor value?

hello! everyone this is my first time in arduino fourm.
I made a security alarm using arduino uno, when the distance decreases by 10 cm, a buzzer attached to pin12 starts.
but i firstly have to set a specific value of distance in code() by taking value from serial monitor but is it possible that arduino can detect a sudden specific change in sensor value, if there is then please tell. my code is below. thankyou in advance.

int trigPin = A5;
int echoPin = A4;
int duration = pulseIn(echoPin, HIGH);
int distance = (duration/2) / 29.1;
int val=155;// change this value for different locations from serial monitor 
void setup() { 
   pinMode(trigPin, OUTPUT);
  pinMode(echoPin, INPUT);
  pinMode(12, OUTPUT);
  // put your setup code here, to run once:
  Serial.begin(9600);
}

void loop() {
  long duration, wait;
   digitalWrite(trigPin, LOW);  
  delayMicroseconds(2);
  digitalWrite(trigPin, HIGH);
  delayMicroseconds(10); 
  digitalWrite(trigPin, LOW);
 duration = pulseIn(echoPin, HIGH);
 distance = (duration/2) / 29.1;delay(10);
 Serial.print(distance);
 Serial.println("cm");delay(10);
 if (val-10>distance) {
  digitalWrite(12,HIGH);
 }

  

}

Describe in words the exact condition you want to detect as a first step for us?

is it possible that arduino can detect a sudden specific change in sensor value,

How much of a change should be regarded as significant ?
What time period will the change be measured over ?