It took a stopping train 41/4min to travel between two stations 11.2km apart.The train accelerated uniformly during the first 11/4min of the journey,and decelerated uniformly to rest during the last 3/2min of the journey.The train had moved with uniform speed during the remaining part of its travel.calculate (a)Uniform speed,km/h (b)Uniform acceleration (c)Uniform retardation (d)Distance travelled in the first 4min of the journey (c)Distance covered in the last 3min of the journey.
assume the maximum velocity was V.
Then the average velocity during starting and stopping was V/2.
So, during starting, you know the avg velocity, and time, so
distancestarting=v/2 * 11/4*1/60 in km if v is in km/hr
distancestopping= v/2*3/2*1/60
distance constant speed=11.2-v/120(11/4+6/4)
time constant speed= 41/4-11/4-3/2 min
convert that to hours.
velocity v= distanceconstantspeed/timeconstant speed
from that calculate v.
Everything else ought to work out easily.
To solve this problem, we will break it down into different parts:
Let's analyze the given information in the problem:
- Total time taken by the train: 41/4 min
- Distance between two stations: 11.2 km
- Acceleration time: 11/4 min
- Deceleration time: 3/2 min
(a) To find the uniform speed:
The total time taken by the train is given as 41/4 min. We need to find the uniform speed, which means the train's speed during the remaining part of its travel.
We can calculate the uniform speed using the formula: Speed = Distance / Time
Since the distance between the two stations is 11.2 km, and the total time taken is 41/4 min, we can substitute these values into the formula:
Speed = 11.2 km / (41/4) min
To simplify the calculation, we can convert the time to the same unit as the distance. As 1 hour = 60 minutes, we can convert the total time to hours:
Total time = 41/4 min = (41/4) * (1/60) hours = 41/240 hours
Now substitute the values into the formula:
Speed = 11.2 km / (41/240) hours
To simplify further, we can multiply the numerator and denominator by the reciprocal of the fraction:
Speed = 11.2 km * (240/41) / 1 hour
Calculating this will give us the answer for the uniform speed in km/h.
(b) To find the uniform acceleration:
The train accelerates uniformly during the first 11/4 min of the journey.
Acceleration is defined as the change in velocity divided by the time taken. Here, we need to find the uniform acceleration while the train is accelerating.
To calculate uniform acceleration, we can use the formula: Acceleration = Change in Velocity / Time
We know that the train accelerates uniformly, so it starts from rest and reaches a certain velocity at the end of 11/4 min.
At the start, the velocity is 0 km/h, and at the end, it reaches the uniform speed we calculated in part (a). So, the change in velocity is equal to the uniform speed.
Acceleration = (Uniform Speed - 0 km/h) / (11/4) min
Again, we need to convert the time to the same unit as the speed. So, 11/4 min = (11/4) * (1/60) hours = 11/240 hours
Substituting the values, we can calculate the uniform acceleration.
(c) To find the uniform retardation:
The train decelerates uniformly to rest during the last 3/2 min of the journey.
Retardation is the opposite of acceleration. So, the uniform retardation is the negative of the uniform acceleration calculated in part (b).
Uniform Retardation = - Uniform Acceleration
(d) To find the distance traveled in the first 4 min of the journey:
We are given that the train accelerates uniformly during the first 11/4 min of the journey. So, we need to find the distance covered during this time period.
To calculate the distance covered during uniform acceleration, we can use the formula: Distance = (Initial Velocity * Time) + (0.5 * Acceleration * Time^2)
In this case, the initial velocity is 0 km/h, the time is 11/4 min, and the acceleration is the same as the uniform acceleration calculated in part (b).
By substituting these values, we can calculate the distance covered during uniform acceleration.
(e) To find the distance covered in the last 3 min of the journey:
We are given that the train decelerates uniformly to rest during the last 3/2 min of the journey. So, we need to find the distance covered during this time period.
To calculate the distance covered during uniform retardation, we can use the same formula as in part (d):
Distance = (Initial Velocity * Time) + (0.5 * Retardation * Time^2)
In this case, the initial velocity is the uniform speed calculated in part (a), the time is 3/2 min, and the retardation is the negative of the uniform acceleration calculated in part (b).
By substituting these values, we can calculate the distance covered during uniform retardation.
Using these steps, you can now calculate the answers to all parts of the question.