PROBLEM ON TRAINS (level - 1)
Q1–10 of 50A speed of 14 metres per second is the same as
Conversion Formula: $\text{km/h} = \text{m/s} \times \frac{18}{5}$
$14 \times \frac{18}{5} = \frac{252}{5} = 50.4\text{ km/h}$
Answer: (c) 50.4 km/hr
A train travelling at a speed of 45 km/h crosses a pole in 24 sec. What is the length of the train?
Speed: $45\text{ km/h} = 45 \times \frac{5}{18} = \frac{25}{2}\text{ m/s}$
Length ($L$): $\text{Speed} \times \text{Time} = \frac{25}{2} \times 24 = 300\text{ m}$
Answer: (b) 300 m
A train covers a distance of 57.6 km in 48 minutes. What is its speed in m/s ?
Distance: $57.6\text{ km} = 57600\text{ m}$
Time: $48\text{ mins} = 48 \times 60 = 2880\text{ s}$
Speed: $\frac{57600}{2880} = 20\text{ m/s}$
Answer: (a) 20
A train travelling at the speed of 144 km/h crossed a platform 100 m long in 30 seconds. Find the length of the train.
Speed: $144\text{ km/h} = 144 \times \frac{5}{18} = 40\text{ m/s}$
Distance: $\text{Speed} \times \text{Time} = 40 \times 30 = 1200\text{ m}$
Length of Train ($L$): $L + 100 = 1200 \implies L = 1100\text{ m} = 1.1\text{ km}$
Answer: (c) 1.1 km
A train moving at a speed of 36 km/hr crosses a standing man in 10 seconds. Find the time taken by it to cross a platform of 60 m.
Speed: $36\text{ km/h} = 36 \times \frac{5}{18} = 10\text{ m/s}$
Train Length ($L$): $10 \times 10 = 100\text{ m}$
Time to cross platform: $\frac{L + \text{Platform}}{v} = \frac{100 + 60}{10} = 16\text{ s}$
Answer: (c) 16 s
A train running at the speed of 60 km/h crosses a pole in 9 seconds. What is the length of the train?
Speed: $60\text{ km/h} = 60 \times \frac{5}{18} = \frac{50}{3}\text{ m/s}$
Train Length ($L$): $\frac{50}{3} \times 9 = 150\text{ m}$
Answer: (a) 150 m
A train of length 350 m takes 96 seconds to cross a tunnel of length 450 meters. What is the speed of train in km/hr?
Total Distance: $350 + 450 = 800\text{ m}$
Speed: $\frac{800}{96}\text{ m/s} = \frac{800}{96} \times \frac{18}{5} = 30\text{ km/h}$
Answer: (c) 30
A train moves with a speed of 108 kmph. Its speed in metres per second is
Conversion Formula: $\text{m/s} = \text{km/h} \times \frac{5}{18}$
$108 \times \frac{5}{18} = 30\text{ m/s}$
Answer: (c) 30 m/sec.
In what time will a train 100 metres long cross an electric pole, if its speed be 144 km / hr?
Speed: $144\text{ km/h} = 144 \times \frac{5}{18} = 40\text{ m/s}$
Time: $\frac{\text{Length}}{\text{Speed}} = \frac{100}{40} = 2.5\text{ s}$
Answer: (a) 2.5 sec
The length of the bridge, which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds, is
Speed: $45\text{ km/h} = 45 \times \frac{5}{18} = \frac{25}{2}\text{ m/s}$
Total Distance: $\frac{25}{2} \times 30 = 375\text{ m}$
Bridge Length ($B$): $375 - 130 = 245\text{ m}$
Answer: (c) 245 m