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Q.

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

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a

10ms−2

b

4ms−2

c

5ms−2

d

2ms−2

answer is D.

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Detailed Solution

Speed, v=vx2+vy2Rate of change of speed,dvdt=2vxdvxdt+2vydvydt2vx2+vy2=vxax+vyayvx2+vy2=(3×2)+(4×1)(3)2+(4)2=2m/s2
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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