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Question

A particle is moving in the xy plane. At certain instant of time, the components of its velocity and acceleration are as follows: vx=3 ms1,vy=4 ms1,ax=2 ms2 and ay=1 ms2. The rate of change of speed at this moment is

A
10 ms2
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B
4 ms2
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C
5 ms2
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D
2 ms2
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Solution

The correct option is D 2 ms2
At a certain instant, v=v2x+v2y
Rate of change of velocity is given by
dvdt=2vxdvxdt+2vydvydt2v2x+v2y
=vxax+vyayv2x+v2y (dvxdt=ax and dvydt=ay)
=3×2+4×132+42
=2 m/s2

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