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Q.

The position of a particle moving along x-axis varies with time ‘t’ given by  xt=10+8t−3t2. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t)= 5−8t3 . At t=1 s, the speed of the second particle as measured in the frame of the first particle is given as  ν. Then ν in (m2/s2)  is _______

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Detailed Solution

Coordinate of particle A = XA=−3t2+8t+10​Differentiating with time will give velocity of particle A​v→A=−6t+8i∧At t=1s, v→A=2i∧​Coordinate of particle B =  YB=5−8t3   ​Differentiating with time will give velocity of particle B  v→B=−24t2j∧​At t=1s, v→B=−24j∧​Speed of B wrt A=v→B−v→A=−24j∧−2i∧=242+22= 580 m/s
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