How to Calculate Time Taken for a Train to Accelerate?
What is the equation needed to calculate the time taken for a train to accelerate?
Given that a locomotive exerts a constant force of 7.8×105 N to accelerate a train to 82 km/h, what is the time taken for the train of mass 1.1×107 kg to reach this speed from rest?
Calculating the Time Taken for a Train to Accelerate
To calculate the time taken for a train to accelerate, we need to use the kinematic equation:
v = u + at
Where:
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
t is the time.
In this case, the train starts from rest (u = 0) and reaches a final velocity of 82 km/h. We need to convert the final velocity to meters per second for consistent units.
The acceleration (a) is given by the force divided by the mass of the train.
Now, we can rearrange the kinematic equation to solve for time (t).
Explanation of Calculating the Time Taken
When a locomotive exerts a constant force of 7.8×105 N to accelerate a train to 82 km/h, we know the values of force and mass of the train.
By using the kinematic equation v = u + at and rearranging it to solve for time (t), we can find that the time taken for the train of mass 1.1×107 kg to reach a speed of 82 km/h from rest is approximately 5.45 minutes.
This calculation involves converting velocity units, determining acceleration, and utilizing the kinematic equation to find the time taken for the train to accelerate. By following these steps, we can accurately calculate the time needed for the train to reach a specific speed from rest.