An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 260 m from the crossing and its speed is 26 m/s. If the engineer's reaction time is 0.51 s, what should be the magnitude of the minimum deceleration to avoid an accident? Answer in units of m/s 2

The right answer is "1.369 m/s²".

Explanation:

The given values are:

Distance (s)

= 260 m

Initial speed (u)

= 26 m/s

Reaction time (t')

= 0.51 s

During reaction time, the distance travelled by locomotive will be:

⇒  

Remained distance between locomotive and car:

⇒  

Now,

The final velocity to avoid collection is, V = 0 m/s

From third equation of motion:

⇒  

On putting the estimated values, we get

⇒  

⇒  

⇒  

⇒            

⇒            

6 cos 34, 6 sin 34 trig

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