Question
A car driver on a straight Mumbai expressway sees a stalled truck m ahead while moving at m/s. His reaction time is s, after which he applies brakes that produce a constant deceleration of m/s. Does the car hit the truck? If yes, at what speed?
Solution — Step by Step
For the first s, the car keeps moving at m/s with no braking. So distance covered m. After this, only m of road is left between the car and the truck.
We need the distance to come to rest from m/s with m/s.
The braking distance is m, which is less than the available m. The car can stop in time.
Total stopping distance from the moment the driver spots the truck m. The truck is m away. The car stops with m to spare.
Final Answer: The car does not hit the truck. It stops m short.
Why This Works
Real-world kinematics problems almost always have a “thinking time” before the action starts. During reaction time, velocity stays constant — no equations of motion needed there, just . Only after braking begins do we use .
The trap most students fall into is treating the entire m as the braking distance. That gives a wrong required deceleration and the wrong final answer. Always split the problem into “before reaction” and “after reaction” phases.
Alternative Method
We can frame it as: what is the minimum reaction time for which the car still stops in time? Stopping distance with full s reaction is m. If reaction time were longer than s, the car would crash. This kind of inverse framing is common in JEE Main.
Do not plug m directly into to find . That ignores the s reaction-time gap and gives a non-zero (wrong) impact speed. The reaction-time distance is part of the total — not extra.
For NEET, examiners often replace “reaction time” with “human response delay” or “perception lag”. Same physics, different vocabulary. Underline these phrases when you read the question.