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A particle is moving in the x-y plane. A...

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

A

`4 m//s^(2)`

B

`2 m//s^(2)`

C

`sqrt3 m//s^(2)`

D

`sqrt5 m//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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