Question

Displacement of a body from my reference point is given by root x is equals to x^1/2 =2t+3 where x is in metres and t is in seconds what is the initial velocity of the body

Answer 1

equation is given as

√x = 2 t + 3

taking square both side

(√x )² = (2 t + 3)²

x = (2 t + 3)²

x = (2t)² + (3)² + 2 (2t) (3)

x = 4 t² + 12 t + 9

taking derivative both side relative to "t"

dx/dt = 2 (4t) + 12

dx/dt = 8 t + 12

we know that , v = dx/dt

hence  v =  8 t + 12

at t = 0

v = 8 (0) + 12

v = 12 m/s

hence the initial velocity is 12 m/s