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
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