Question #21281

The velocity of a body moving along x-axis is given by v =(36+2x)^1/2 where v is in m/s and x is in metre.Find distance travelled by it in 2nd second.

Expert's answer

v=dx/dt

dx/dt=(36+2x)^1/2

dx(36+2x)^-1/2=dt

(1/2)*2*(36+2x)^1/2=t+const

if x(0)=0 36^1/2=const

const=6

x=(t+6)^2/2-18

d=x(2)-x(0)=(64/2-18)-(36/2-18)=14 m

dx/dt=(36+2x)^1/2

dx(36+2x)^-1/2=dt

(1/2)*2*(36+2x)^1/2=t+const

if x(0)=0 36^1/2=const

const=6

x=(t+6)^2/2-18

d=x(2)-x(0)=(64/2-18)-(36/2-18)=14 m

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