The coordinates of a particle moving in XY-plane at any instant of time t are `x=4t^(2),y=3t^(2)`. The speed of the particle at that instant is

Options

A. 10 t
B. 5 t
C. 3 t
D. 2 t

Answer

A

Explanation

As, position vector, `r=xhati+yhatj`
`r=4t^(2)hati+3t^(2)hatj`
Velocity `v=(dr)/(dt)=4(2t)hati+3(2t)hatj`
or `" "v=8thati+6thatj`
`:.` Speed `=|v|`
`=sqrt(64t^(2)+36t^(2))`
`=sqrt(100t^(2))=10t`