a train starts from rest and accelerates uniformly at 100m/min^2 for 10 min. it then maintains a constant velocity for 20 minutes. the brakes are applied and then the train is uniformly retarded. it comes to rest in 5 minutes.find the velocity retarded and distance travelled.
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Explanation:
Since body starts from rest so,
initial velocity, u = 0m/min
Given, uniform acceleration, a = 100m/min
Time = 10min
Distance travelled during acceleration = S = ut + 1/2at²
S = 0×10 +1/2×100×10×10
S = 5000m
Velocity acquired = ?
Using formula,
v = u + at
v = 0 + 100*10
v = 1000m/min
Distance travelled with constant velocity, S = v × t
S = 1000×20
S = 20,000m
Given, that the train stops so,
Final velocity, v = 0m/min
Initial velocity, u = 1000m/min
Time = 5min
Retardation = ?
Using formula,
v = u + at
0 = 1000 + 5a
a = - 200m/min²
Retardation = 200m/min²
Distance travelled during retardation, S = ut - 1/2at²
S = 1000×5 - 1/2×200×5×5
S = 5000 - 2500
S = 2500m
Total Distance covered = 5000 + 20,000 + 2500
= 27,500m
= 27.5km
Distance covered = 27.5km
Answer:
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