Question

A train starts from station A and reaches Station B after 10000 s But didn't stop at Station B . If it reaches Station B with a constant acceleration of 1m/s², find the distance between A and B.
If the train was carrying 10 wagons of 10000 kg each, find the Force applied by the train.
Find the work done by the train.
Find the power generated by the train.

Answer 1

Given :

• Initial velocity of train = 0 m/s
• Acceleration = 1m/s²
• Time take to reach Station B = 10,000s
• Mass of 1 wagon = 10000 kg
• No. of wagons = 10

To Find :

We have to find the following related to the train :

a] Distance between A and B

b] Force applied by the train .

c] work done by train to reach station B

d] The power generated by the train

Formula To be Applied :

We will use the following formulas related to dynamics :

• S = ut+½at²
• Force = mass×acceleration
• Work = Force×displacement
• Power = work/time

Process :

First, We will find the distance of the two station by using the formula stated above, then we will find the total mass of the train . then after this , we will calculate the Force applied by the train using the formula stated above, then through Force we can find the work done by the train to reach station B.

Now, with the work , we can find the power generated by the train.

Solution :

Given, Mass of each wagon = 10000 kg

Total no. of wagons = 10

Hence, total mass of wagon = 10×10000 kg

= 1,00,000 kg

Initial Velocity = 0m/s

Acceleration = 1m/s²

Hence, S = ut+½at²

$\tt{ \implies s = (0 \times 10000) + \frac{1}{2} \times 1 \times 10000 \times 10000}$

$\implies \tt{s = 0 + (10000 \times 5000)}$

$\tt{ \implies s = 50000000 \: m}$

Hence, Distance of A and B = 5,00,00,000 m

or, Distance between A and B = 50,000 Km

Given, Mass = 1,00,000 kg

Acceleration = 1m/s²

Hence, Force = Acceleration × Mass

$\implies \tt{force = 1 \times 100000}$

$\tt{ \implies force = 100000}$

Hence, Force = 100000 N

Now, this is the work Done :

Given, Force = 1,00,000 N

Distance = 5,00,00,000 m

Hence, Force = Force×displacement

$\tt{ \implies work = 100000 \times 50000000}$

$\implies \tt{work = 5000000000000}$

Hence, Work = 5000000000000

or, Work = 5×10¹² J

Now, we will calculate the power generated:

Given, Work done = 5×10¹² J

time = 10,000 seconds

Hence, Power = Work/time

$\implies \tt{power = \frac{5 \times {10}^{12} }{ {10}^{4} } }$

$\implies \tt{power = 5 \times {10}^{12 - 4}}$

$\implies \tt{power = 5 \times {10}^{8}}$

Hence, Power = 5×10⁸ W

Or, power = 5×10⁵ Kw

__________________________

Additional Information:

These are some formulas relayed to dynamics and kinematics:

1] Dynamics :

• Force = mass × acceleration
• Momentum = velocity × mass
• Impulse = Force × time
• Work = distance × force
• Power = work/time
• Kinetic Energy = ½mv²

2] Kinematics

• acceleration = (v-u)/t
• v = u+at
• s = ut+½at²
• v²-u² = 2as

Answer 2

Answer:

Explanation:

A train starts from station A and reaches Station B after 10000 s But didn't stop at Station B . If it reaches Station B with a constant acceleration of 1m/s², find the distance between A and B.

If the train was carrying 10 wagons of 10000 kg each, find the Force applied by the train.

Find the work done by the train.

Find the power generated by the train.