Question

The Velocity Of A Particle Moving In Positive X Direction In According To Relation V=Underoot 4X If At T=0 Particle Is At X=0 Then The Velocity And Acceleration At T=2 Sec Is

Answer 1

Answer:

Velocity = 4 m/s

Acceleration = 2 m/s²

Explanation:

The Velocity Of A Particle Moving In Positive X Direction In According To Relation V=Underoot 4X If At T=0 Particle Is At X=0 Then The Velocity And Acceleration At T=2 Sec Is

v = √4x

=> v = 2√x

v = dx/dt

=> dx/dt = 2√x

=> dx/√x = 2dt

=> integrating both sides

=> 2√x = 2t + c   ( c is onstant)

at t = 0   x= 0

=> 2*0 = 2*0 + c

=> c = 0

=> 2√x = 2t

=> √x = t

=> x = t²

x at t = 2 => x = 4

v = 2√x

v = 2√4

v = 4

Velocity = 4 m/s

a = dv/dt = d(2√x)/dt

putting x = t²

=> a = d(2t)/dt

=> a = 2

Acceleration = 2 m/s²  (independent of t)