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A particle moves in such a manner that x...

A particle moves in such a manner that `x=At, y=Bt^(3)-2t, z=ct^(2)-4t`, where x, y and z are measured in meters and t is measured in seconds, and A, B and C are unknown constants. Give that the velocity of the particle at `t=2s` is `vec(v)=((dvec(r))/(dt))=3hat(i)+22hat(j) m//s`, determine the velocity of the particle at `t=4s`.

Text Solution

Verified by Experts

The correct Answer is:
`(3hat(i)+94hat(j)+4hat(k)) m//s`
`vec(v)=Ahat(i)+(3Bt^(2)-2)hat(j)+(2ct-4)hat(k)`
At `t=2, Ahat(i)+(12B-2)hat(j)+(4c-4)hat(k)=3hat(i)+22hat(j)`
Thus, `A=3, B=2, C=1`
`:. Vec(v)=3hat(i)+(6t^(2)-2)hat(j)+(2t-4)hat(k)`
At `t=4, vec(v)=3hat(i)+(96-2)hat(j)+(8-4)hat(k)=3hat(i)+94hat(j)+4hat(k)`
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