It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________
Train Speed Calculation Using Length and Time
To find the difference in the speeds of the two trains, we first need to calculate the individual speed of each train using the formula:
$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $
When a train passes a telegraph post, the distance covered is equal to the length of the train itself.
Calculating Speed of Train 1
- Given: Length ($L_1$) = 120 m, Time ($t_1$) = 10 s
- Calculation: Speed ($S_1$) = $L_1 / t_1$
- $ S_1 = \frac{120 \text{ m}}{10 \text{ s}} = 12 \text{ m/s} $
Calculating Speed of Train 2
- Given: Length ($L_2$) = 150 m, Time ($t_2$) = 15 s
- Calculation: Speed ($S_2$) = $L_2 / t_2$
- $ S_2 = \frac{150 \text{ m}}{15 \text{ s}} = 10 \text{ m/s} $
Difference in Train Speeds
- Objective: Find the magnitude of the difference between $S_1$ and $S_2$.
- Calculation: Difference = $|S_1 - S_2|$
- $ \text{Difference} = |12 \text{ m/s} - 10 \text{ m/s}| = 2 \text{ m/s} $
The magnitude of the difference in the speeds of the two trains is 2 m/s.
Important Questions from Speed Time and Distance
A train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
A car travels from a place X to place Y at an average speed of v km/hr from y to X at an average speed of 2v km/hr, again from X to y at an average speed of 3v km/hr and again from y to x at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
