Importance of vision; acceleration numerical

Importance of vision to road users

About 90 percent of the information a road user needs (road alignment, signs, signals, other vehicles, pedestrians and hazards) is received through the eyes, so vision is the most important sense in driving. Defective vision causes late detection, wrong judgement of speed and distance, and crashes.

• Visual acuity decides the distance at which signs and objects can be read; sign letter heights are fixed to suit it.
• Field of vision (clear cone about 3-5 degrees, fairly clear up to 10-12 degrees, peripheral up to about 120-160 degrees) fixes where signs are placed; it narrows with speed.
• Colour vision is needed to read red, amber and green signals.
• Glare vision and recovery affect night driving; they decide anti-glare design and lighting.
• Depth perception is needed for judging gaps when overtaking and crossing.
• Night vision needs street lighting, retro-reflective signs and markings.

Therefore design provides adequate sight distance (IRC:66, IRC:SP:23), legible signs (IRC:67), lighting and markings (IRC:35).

Numerical

Given $\dfrac{dv}{dt} = 2 - 0.04v$ (v in m/s), initial speed $v_0 = 100$ km/h $= 27.78$ m/s.

Since $a = 2 - 0.04v$, differentiating gives $\dfrac{da}{dt} = -0.04\,\dfrac{dv}{dt} = -0.04a$, so

$$a(t) = a_0 e^{-0.04t},\qquad a_0 = 2 - 0.04(27.78) = 0.889\ \text{m/s}^2$$

For $a = 1.0$ m/s$^2$ the speed would have to be $v = (2-1)/0.04 = 25$ m/s $= 90$ km/h:

$$t = \frac{1}{0.04}\ln\frac{a_0}{1.0} = 25\ln(0.889) = -2.94\ \text{s}$$

Answer: the acceleration at the start (100 km/h) is only 0.889 m/s$^2$, and it keeps falling as the vehicle speeds up, so it never reaches 1.0 m/s$^2$ afterwards. The acceleration was 1.0 m/s$^2$ about 2.94 s before the 100 km/h instant (t = -2.94 s, when the speed was 90 km/h). The value 1.0 m/s$^2$ is reached after time zero only if the vehicle starts below 90 km/h (25 m/s); for example, from rest $t = 25\ln 2 = 17.33$ s.