A particle is moving in the x−y plane. At certain instant of time, the components of its velocity and acceleration are as follows: vx=3ms−1,vy=4ms−1,ax=2ms−2 and ay=1ms−2. The rate of change of speed at this moment is
A
√10ms−2
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B
4ms−2
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C
√5ms−2
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D
2ms−2
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Solution
The correct option is D2ms−2 At a certain instant, v=√v2x+v2y
Rate of change of velocity is given by dvdt=2vxdvxdt+2vydvydt2√v2x+v2y =vxax+vyay√v2x+v2y(∵dvxdt=axanddvydt=ay) =3×2+4×1√32+42 =2m/s2