While traveling at 90 km/hr, a train engineer suddenly notices a car stopped on the track at a level crossing, 700 m ahead of the train. She immediately applies the brakes, slowing the train down with a constant deceleration of a = - 0.5 m/s²

a) How far from the car will the train come to a complete rest?

b) Assume that the train was going faster than 90 km/hr initially, but that the deceleration was still a = - 0.5 m/s². What is the minimum initial speed of the train such that it would have hit the car?

Solution:

a) v² = v₀² + 2 a x

v₀ = (90 km/hr)(1hr/3600 s)(10³m/km) = 25 m/s

v = 0     (at rest)

          thus

0 = (25 m/s)² + 2(-0.5 m/s²) x

x = 625 m

         therefore the train travels

700 m - 625 m = 75 m

b) Now we want   v=0   at   x= 700 m   for the train to just hit the car, therefore

v² = v₀² + 2 a x

0 = v₀² + 2(-0.5 m/s²)(700 m)

v₀² = 700 m²/s²

v₀ = 26.46 m/s

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