Imagine a car or truck speeding away in front of you on the road. Here is a rough method to estimate its distance and speed using your outstretched hand (try this as a passenger, not a driver!).
At any given time its distance away is approximately
We use the figure below to estimate angles based on our outstretched hand at arm’s length:
Hence a vehicle that is 2m wide subtending an angle of 5 degrees (3 fingers at arm’s length) is about 23m away. At 1 degree (1 little finger at arm’s length) it is about 115m away.
Then measure the time T (in seconds) it takes to go from 3 fingers width (5 degrees) to 1 little finger width (1 degree) at arm’s length. Its relative speed in km/h is approximately given by
For example, if a 2m-wide car takes 33 seconds to go from 3 fingers to 1 little finger width at arm’s length (115-23=92 m in distance), it is going 10km/h faster than I am.
To justify these formulas, the figure below shows segment BC of width w at distance d from A, subtending an angle of 
Formula (1) then follows from 
Formula (2) is true since we are covering a distance 
The table below shows some sample values for a car with width 2m and truck with width 3m.
| Angle subtended by object (degrees) | Width of vehicle (m) | Distance of object (m) | Approximate distance using (1) |
| 20 | 2 | 5.7 | 5.7 |
| 10 | 2 | 11 | 11 |
| 5 | 2 | 23 | 23 |
| 1 | 2 | 115 | 114 |
| 0.02 | 2 | 5730 | 5700 |
| 20 | 3 | 8.5 | 8.6 |
| 10 | 3 | 17 | 17 |
| 5 | 3 | 34 | 34 |
| 1 | 3 | 172 | 171 |
| 0.02 | 3 | 8600 | 8550 |
The smallest angle of 0.02° (~1 minute) approximately corresponds to the smallest object we can resolve with the naked eye.
The next table shows estimates of receding speeds based on going from 5° to 1° of angular diameter.
| Width of vehicle (m) | Time (s) to go from 5° to 1° | Estimated speed (km/h) |
| 2 | 3 | 110 |
| 2 | 5 | 66 |
| 2 | 10 | 33 |
| 2 | 33 | 10 |
| 3 | 5 | 99 |
| 3 | 10 | 50 |
| 3 | 33 | 15 |
Reference:
Chaitanya's Random Pages 