Anthony Pitt
Mar 1
Q?
Find the minimum time for a train to travel between stopping places 2km apart if the acceleration is 1m/s , the deceleration is 1m/s and the speed constant at 72 m/h during the intervening period
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ChatGPT
Mar 1
To find the minimum time for the train to travel between stopping places 2km apart, we need to calculate the time it takes for the train to accelerate to its constant speed, travel at that speed, and then decelerate to a stop.
First, let's convert the distance between the stopping places from kilometers to meters:
2 km = 2000 meters
1. Acceleration phase:
Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the time it takes for the train to accelerate to its constant speed:
72 m/h = 20 m/s (since 1 m/s = 3.6 km/h)
0 = 0 + 1t
t = 20 seconds
2. Constant speed phase:
The train travels at a constant speed of 72 m/h for a certain distance. We can calculate the time it takes to cover the distance of 2000 meters at this speed:
t = d/v
t = 2000/20
t = 100 seconds
3. Deceleration phase:
Using the same formula v = u + at, we can calculate the time it takes for the train to decelerate to a stop:
0 = 20 - 1t
t = 20 seconds
Therefore, the total time for the train to travel between stopping places 2km apart is:
20 seconds (acceleration) + 100 seconds (constant speed) + 20 seconds (deceleration) = 140 seconds
So, the minimum time for the train to travel between stopping places 2km apart is 140 seconds.
First, let's convert the distance between the stopping places from kilometers to meters:
2 km = 2000 meters
1. Acceleration phase:
Using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the time it takes for the train to accelerate to its constant speed:
72 m/h = 20 m/s (since 1 m/s = 3.6 km/h)
0 = 0 + 1t
t = 20 seconds
2. Constant speed phase:
The train travels at a constant speed of 72 m/h for a certain distance. We can calculate the time it takes to cover the distance of 2000 meters at this speed:
t = d/v
t = 2000/20
t = 100 seconds
3. Deceleration phase:
Using the same formula v = u + at, we can calculate the time it takes for the train to decelerate to a stop:
0 = 20 - 1t
t = 20 seconds
Therefore, the total time for the train to travel between stopping places 2km apart is:
20 seconds (acceleration) + 100 seconds (constant speed) + 20 seconds (deceleration) = 140 seconds
So, the minimum time for the train to travel between stopping places 2km apart is 140 seconds.
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