A goods train passes through a station at a steady speed of 10 m s –1 at time t = 0. An expresstrain is at rest at the station. The express train leaves the station with a uniform acceleration of0.5 m s –2 just as the goods train goes past. Both trains move in the same direction on straight,parallel tracks.At which time t does the express train overtake the goods train?A 6 s B 10 s C 20 s D 40 s
Question
A goods train passes through a station at a steady speed of 10 m s –1 at time t = 0. An expresstrain is at rest at the station. The express train leaves the station with a uniform acceleration of0.5 m s –2 just as the goods train goes past. Both trains move in the same direction on straight,parallel tracks.At which time t does the express train overtake the goods train?A 6 s B 10 s C 20 s D 40 s
Solution
To solve this problem, we need to set the distances travelled by both trains equal to each other and solve for time.
The distance travelled by the goods train is given by the equation: d1 = v*t where v is the speed of the goods train (10 m/s) and t is the time.
The distance travelled by the express train is given by the equation: d2 = 0.5at^2 where a is the acceleration of the express train (0.5 m/s^2) and t is the time.
Setting d1 = d2, we get: 10t = 0.50.5t^2 Solving for t, we get t = 20 seconds.
So, the express train overtakes the goods train at t = 20 seconds. The answer is C.
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