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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

`sqrt(10)ms^(-2)`

B

`4ms^(-2)`

C

`sqrt(5)ms^(-2)`

D

`2ms^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Speed , `v=sqrt(v_(x)^(2)+v_(y)^(2))`
Rate of change of speed.
`(dv)/(dt) =(2v_(x)(dv_(x))/(dt)+2v_(y)(dv_(y))/(dt))/(2sqrt(v_(x)^(2)+v_(y)^(2)))=(v_(x)a_(x)+v_(y)a_(y))/(sqrt(v_(x)^(2)+v_(y)^(2)))`.
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