Stopping Distance

Stopping Distance Includes Reaction and Braking Distance

Stopping distance is the total distance a moving object needs until it fully stops. For a vehicle, it starts before the brakes act.

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 Uses Constant Deceleration

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.

Braking Distance Grows with the Square of Speed

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 $v^2$ . For a fixed vehicle mass, kinetic energy $K=\frac{1}{2}mv^2$ also scales with the square of speed. The brakes and tire-road forces must remove that energy while bringing the vehicle to rest.

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 doubles, reaction distance doubles from $10\text{ m}$ to $20\text{ m}$ , while braking distance quadruples from $10\text{ m}$ to $40\text{ m}$ . Their sum therefore rises from $20\text{ m}$ to $60\text{ m}$ .

Calculating Total Stopping Distance

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}

Under those conditions, the model gives a stopping distance of $60\text{ m}$ .

That $60\text{ m}$ includes two parts. The first $20\text{ m}$ happens before braking starts, and the next $40\text{ m}$ happens while the vehicle is braking.

This calculation shows how the formula works. A real stopping distance changes with perception-reaction time, road surface, tires, weather, grade, and braking performance. One design example uses a $2.5\text{ s}$ perception-reaction time and $3.4\text{ m/s}^2$ deceleration.