Stopping Distance

Stopping Distance Is More Than Braking Distance

Stopping distance is the total distance a moving object needs until it fully stops. For a vehicle, this distance does not only happen while the brakes are acting.

Before braking begins, the driver still needs reaction time. During that time, the vehicle keeps moving forward with its initial speed.

d_{\text{stop}}=d_{\text{reaction}}+d_{\text{brake}}

So stopping distance has two stages. The first stage happens when the driver notices danger but the vehicle has not started braking. The second stage happens after the brakes act and the vehicle slows to a stop.

Part	What Happens	What Determines It
Reaction distance	The vehicle still moves with its initial speed	Speed and reaction time
Braking distance	The vehicle slows until it stops	Initial speed and deceleration magnitude

Car Stopping Distance

Change the initial speed to compare green reaction distance with orange braking distance.

Initial speed: $20\text{ m/s}$
Reaction distance: $20\text{ m}$
Braking distance: $40\text{ m}$
Stopping distance: $60\text{ m}$

Braking Distance Comes from Uniform Acceleration

While the brakes act, the vehicle slows down. If the deceleration is treated as constant and the final velocity is zero, a uniformly accelerated motion equation can be used to find the braking distance.

v_t^2=v_0^2+2a\Delta x

The quantity $b$ is the magnitude of the deceleration, so it is written as a positive value.

This formula uses a simple assumption: the path is straight, braking deceleration is treated as constant, and the vehicle does not skid. If the road condition changes, the value of $b$ can change too.

Speed Makes Stopping Distance Grow Quickly

Reaction distance is directly proportional to speed. If the speed doubles, the reaction distance also doubles for the same reaction time.

Braking distance is more sensitive because it contains $v^2$ . As speed increases, the motion energy that must be removed by the brakes grows much more quickly.

Suppose the reaction time is $1\text{ s}$ and the braking deceleration magnitude is $5\text{ m/s}^2$ .

Speed	Reaction Distance	Braking Distance	Stopping Distance
$10\text{ m/s}$	$10\text{ m}$	$10\text{ m}$	$20\text{ m}$
$20\text{ m/s}$	$20\text{ m}$	$40\text{ m}$	$60\text{ m}$
$30\text{ m/s}$	$30\text{ m}$	$90\text{ m}$	$120\text{ m}$

When speed rises from $10$ to $20\text{ m/s}$ , stopping distance rises from $20$ to $60\text{ m}$ . It is not just doubled because the braking part follows the square of speed.

Safe Space Before a Vehicle Stops

A vehicle moves at $20\text{ m/s}$ . The driver's reaction time is $1\text{ s}$ and the magnitude of the braking deceleration is $5\text{ m/s}^2$ .

d_{\text{reaction}}=20(1)=20\text{ m}

So the vehicle needs $60\text{ m}$ to stop under those conditions.

That $60\text{ m}$ is not only the distance after the brakes are pressed. The first $20\text{ m}$ happens before braking starts, and the next $40\text{ m}$ happens while the vehicle is braking.