Question:
An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:
$\sqrt{\frac{\mathrm{v}^{2}+\mathrm{u}^{2}}{2}}$
$\frac{\mathrm{v}-\mathrm{u}}{2}$
$\frac{u+v}{2}$
$\sqrt{\frac{\mathrm{v}^{2}-\mathrm{u}^{2}}{2}}$
Correct Option: 1
Solution:
$\left(\mathrm{v}^{\prime}\right)^{2}=\mathrm{u}^{2}+2 \mathrm{ad}$'
$v^{2}=\left(v^{\prime}\right)^{2}+2 a d$
solving, we get
$\mathrm{v}^{\prime}=\sqrt{\frac{\mathrm{v}^{2}+\mathrm{u}^{2}}{2}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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