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The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.?
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The engine of a train passes an electric pole with a. Velocity u and t...
Given:
To find: Velocity with which the midpoint of the train passes the pole
Explanation:
Answer: The velocity with which the midpoint of the train passes the pole is given by v_m = u + (u*(v-u)^2)/(2L*(
- Velocity of the engine (u)
- Velocity of the last compartment (v)
- Acceleration is uniform
To find: Velocity with which the midpoint of the train passes the pole
Explanation:
- Let L be the length of the train
- Let T be the time taken to cross the pole
- Let M be the midpoint of the train
- At t = 0, the engine is at the pole and the distance between the engine and the midpoint is L/2
- Let a be the acceleration of the train
- Using the equations of motion, we have:
- v = u + a*T
- L = u*T + (1/2)*a*T^2
- Substituting v = u + a*T in the second equation, we get:
- L = u*T + (1/2)*a*(v-u)^2/a^2
- L = u*T + (v-u)^2/2a
- Substituting T = L/(v+u) in the above equation, we get:
- L = u*L/(v+u) + (v-u)^2/2a
- L*(v+u) = u*L + (v-u)^2/2a*(v+u)
- 2a*L*(v+u) = 2u*(v-u)^2 + a*(v+u)^2*L
- 2a*L*v + 2a*L*u = 2u*(v^2 - 2u*v + u^2) + a*(v^2 + 2uv + u^2)*L
- 2a*L*v - 2a*L*u = 2u*(v^2 - 2u*v + u^2) + a*(v^2 + 2uv + u^2)*L
- a*L*(v+u) = u*(v-u)^2
- a = (u*(v-u)^2)/(L*(v+u))
- Using the equation of motion, v = u + a*T, we can find the velocity of the midpoint of the train when it crosses the pole:
- v_m = u + a*(T/2)
- v_m = u + (u*(v-u)^2)/(2L*(v+u))
Answer: The velocity with which the midpoint of the train passes the pole is given by v_m = u + (u*(v-u)^2)/(2L*(
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The engine of a train passes an electric pole with a. Velocity u and t...
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The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.?
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The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.?.
The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The engine of a train passes an electric pole with a. Velocity u and the last compartment of the train crosses the same pole with the velocity v. Then find the velocity with which the midpoint of the train passes the pole. Assuming acceleration to be uniform.?.
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