A train starting from a railway station and moving with uniform accele...
Given:
The train starts from a railway station and moves with uniform acceleration.
It attains a speed of 40 km/hr in 10 minutes.
To Find:
We need to find the acceleration of the train.
Approach:
We can use the formula for acceleration to find the value. The formula is:
Acceleration (a) = Change in Velocity (v) / Time Taken (t)Step 1: Convert Units
First, we need to convert the given speed from km/hr to m/s, as the SI unit of acceleration is m/s².
1 km/hr = 1000 m/3600 s = 5/18 m/s
So, the speed of the train in m/s is:
Speed (v) = 40 km/hr * (5/18) m/s = 200/18 m/s ≈ 11.11 m/s
Step 2: Convert Time
The given time is in minutes, but we need to convert it to seconds to match the SI unit of acceleration.
Time (t) = 10 minutes * 60 seconds/minute = 600 seconds
Step 3: Calculate Acceleration
Now, we can substitute the values into the formula for acceleration:
Acceleration (a) = Change in Velocity (v) / Time Taken (t)
Acceleration (a) = (Final Velocity - Initial Velocity) / Time Taken
Acceleration (a) = (11.11 m/s - 0 m/s) / 600 seconds
Acceleration (a) = 11.11 m/s / 600 seconds
Acceleration (a) ≈ 0.0185 m/s²
Conclusion:
The acceleration of the train is approximately 0.0185 m/s².