Question

a particle is moving along x axis with uniform acceleration and its velocity is given by v = under root 9+ 6x here x denotes the position of particle on x axis. then the position of particle in metre at t = 2 (assume that at t=0, x=0)​

Answer 1

Answer:

here,

v=√(9+6x)

or,dx/dt=√(9+6x)

[1/{√(9+6x)]dx=dt

integrating both sides with limits at t=0,x=0and at t=2,x=s(sy)

$\int\limits^s_0 {\frac{1}{(9+6x)^{1/2} } } \, dx =\int\limits^2_0 {} \, dt$

or,(√(6s+9))/3-1=2

√(6s+9)=9

squaring on both sides

6s+9=81

or,6s=72

∴s=12m

so distance travelled will be 12 m at t=2s