A particle is moving along the x-axis with its coordinate with the time t given by x(t)=-3t2+8t+10meter. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t)=5-8t3meter. . At t=1 second , the speed of the second particle as measured in the frame of the first particle is given as v . Then v(ms-1) is

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A particle is moving along the x-axis with its coordinate with the time t given by x(t)=-3t2+8t+10meter. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t)=5-8t3meter. . At t=1 second , the speed of the second particle as measured in the frame of the first particle is given as       v   . Then v(ms-1) is

Gazzuolabps · Accepted Answer

The velocity of particles A                                          v            A                    →                            =                                                v          x                                  =                              d            x                                d            t                          =        =                          (        −        6        t                          +                          8        )                            o        r                                                                                                v                A                            →                                            t            =            1                                      =                    (        -        6        +        8        )                                                                  =                    2                          m                  s                      -            1                                                                                                    ⇒            v      A        →          =  +  2      i    ^          m      s          -      1      The velocity of particles B                                          v            B                    →                            =                                                                v            y                                          =                                    d              y                                      d              t                                =                                (          -          24                      t            2                    )                                    o        r                                                                                                v                B                            →                                            t            =            1                                      =                              (          -          24          )                                m                      s                          -              1                                            ⇒            v      B        →          =  -  24      j    ^          m      s          -      1      Speed of the particle B with respect to A,  ⇒            v              B        A              →          =  (            v      B        →          -            v      A        →    )        =  (        -  24      j    ^          -  2      i    ^          )        =  (        -  2      i    ^          -  24      j    ^          )      The magnitude of the velocity  |            v              B        A              →          |  =                    (        2        )            2                  +                  (        24        )            2                          |            v              B        A              →          |  =      v              ⇒      v          =      580        ⇒                                v  =  580        m      s          -      1

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