A particle is moving in the x-y plane. At certain instant of time, the components of its velocity and acceleration are as follows: `v_(x)=3ms^(-1), v_(y)=4ms^(-1), a_(x)=2ms^(-2) and a_(y)=1ms^(-2)`. The rate of change of speed at this moment is

Options

A. `4 m//s^(2)`
B. `2 m//s^(2)`
C. `sqrt3 m//s^(2)`
D. `sqrt5 m//s^(2)`

Answer

B

Explanation

speed `v = sqrt(v_(x^(2)) + v_(y^(2))) :, 2v (dv)/(dt) = 2v_(x)a_(x) + 2v_(y)a_(y)`
`(dv)/(dt) = (v_(x)a_(x) + v_(y)a_(y))/(v) = (3 xx 2 + 4 xx 1)/(sqrt(3^(2) + 4^(2))) = 2 m//s^(2)`