To calculate the stopping distance of a vehicle, we need to know the initial velocity of the vehicle, its final velocity (zero, as it comes to a stop), and the deceleration (negative acceleration) of the vehicle.
Let's assume the initial velocity of the vehicle is "u" (in meters per second), the final velocity is "v" (zero in this case), and the deceleration is "a" (in meters per second squared). The stopping distance "s" (in meters) can be calculated using the following equation:
s = (v^2 - u^2) / (2 * a)
Since the final velocity is zero, the equation simplifies to:
s = -u^2 / (2 * a)
Now, if the initial velocity of the vehicle becomes three times its original value, we can express it as:
u' = 3u
Substituting this into the stopping distance formula:
s' = -(3u)^2 / (2 * a)
s' = -9u^2 / (2 * a)
The stopping distance, "s'," with the velocity three times its original value will be nine times larger than the original stopping distance, "s." The negative sign indicates that the vehicle is coming to a stop, so the value is positive in magnitude. This result assumes that the deceleration remains constant throughout the stopping process. Keep in mind that in real-world scenarios, factors like friction, road conditions, and braking efficiency can influence the actual stopping distance.