Moving along the X-axis there are two points with `x=10+6t,x=3+t^(2)`. The speed with which they are reaching from each other at the time of encounter is (`x` is cm and `t`is in second)

Options

A. `16cms^(-1)`
B. `20cms^(-1)`
C. `8cms^(-1)`
D. `12cms^(-1)`

Answer

C

Explanation

They wil encounter if
`10+6t=3+t^(2)impliest^(2)-6t-7=0impliest=7`
At `t=7s`, speed of first point `v_(1)`
`d/(dt)(10+6t)=6cms^(-1)`
At `t=-7s`, speed of second point `v_(2)`
`d/(dt)(3+t^(2))=2t=2xx7=14cms^(-1)`
`:.` Relsultant velocity `-v_(2)-v_(1)=14-6=8cms^(-1)`