Nine Kilometres to the Barrier
At 22:04 a motorcycle with two riders passes a PCR naka on the straight 9 km road from the Sector 29–31 light point to the barrier at the Sector 47 turn. The constable notes the time and reports a suspected snatching vehicle. A PCR van standing at the same naka starts at 22:07. On paper the van can do 66 km/h, but with a cold engine, traffic and the road's curves its realistic average is 60 km/h. The motorcycle is estimated at 48 km/h. The van's driver says he will 'easily catch them before the barrier'. The barrier has two constables and a spike strip but no vehicle.
1. Calculate whether the van catches the motorcycle before the 9 km barrier. Give the head start, the closing speed, and the time and place of any interception.
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Convert to km per minute: motorcycle 48 km/h = 0.8 km/min; van 60 km/h = 1.0 km/min.
- Head start: the van starts 3 minutes late, so the motorcycle is already 3 × 0.8 = 2.4 km ahead.
- Closing speed: 1.0 − 0.8 = 0.2 km/min.
- Time to close 2.4 km: 2.4 ÷ 0.2 = 12 minutes.
- Distance the van must travel: 12 × 1.0 = 12 km.
The barrier is only 9 km away, so a 12 km pursuit never happens - the van would draw level 3 km beyond it, if the motorcycle kept going. Check the barrier's own timing: the motorcycle reaches it at 9 ÷ 0.8 = 11.25 minutes after 22:04, about 22:15:15. The van reaches it at 22:07 + 9 minutes = 22:16:00. The driver's 'easily catch' overshoots by about 45 seconds at the barrier and by 3 km in the pursuit. The barrier is the intercepting force and must be alerted first.
2. What if the van had started at 22:06 instead? Recalculate and state the operational lesson.
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One minute earlier changes everything:
- Head start at 22:06 = 2 minutes × 0.8 = 1.6 km.
- Time to close = 1.6 ÷ 0.2 = 8 minutes.
- Van distance = 8 × 1.0 = 8 km, which is inside the 9 km road.
Interception at about 22:14, 8 km from the naka and roughly 1 km short of the barrier. The motorcycle's own distance at that moment is 10 minutes × 0.8 = 8 km, which matches.
Operational lessons: the three-minute delay decided the case, and at 22:05 the better decision was a radio message to the barrier giving direction, speed, time and description. A pursuit is a bet on relative speed; a barrier is a bet on the road ending. Alert the barrier even while starting the chase, and log the exact start time, because that one minute will be questioned later.
3. What constant speed would the van have needed to intercept exactly at the barrier, and why is that figure unrealistic?
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For an interception exactly at the barrier, the van must cover 9 km in the 8.25 minutes the motorcycle needs for the remaining 6.6 km (from 22:07 to 22:15:15).
Required speed = 9 ÷ (8.25 ÷ 60) = 9 × 60 ÷ 8.25 ≈ 65.45 km/h.
That is above the 60 km/h realistic average and very close to the van's paper maximum of 66. It leaves no margin for a slow tractor, a red light or a pillion rider forcing a stop, and it assumes the van is already rolling at 22:07. So the honest answer to the driver is: the van cannot be relied on to intercept; the barrier can. The required-average figure belongs in the inquiry report as a check on the driver's claim, not as a justification for a high-speed chase on a city road at 22:00.