Q 21. Displacement vector is given here. \[ r =3.0 t \hat{ i }+2.0 t^{2} \hat{ j }+5.0 \hat{ k } \] The velocity vector will be.. (a) \( 3.0 i +4.0 j \) (b) \( 3.0 i +4.0 t j \) (c) \( 3.0 t i +4.0 j \) (d) \( 3.0 t i +4.0 t j \)
Q 21. Displacement vector is given here. \[ r =3.0 t \hat{ i }+2.0 t^{2} \hat{ j }+5.0 \hat{ k } \] The velocity vector will be.. (a) \( 3.0 i +4.0 j \) (b) \( 3.0 i +4.0 t j \) (c) \( 3.0 t i +4.0 j \) (d) \( 3.0 t i +4.0 t j \)
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Given r = 3.0 t i + 2.0 t2 j + 5.0
differentiating both sides with respect to time t,
dr/dt = d/dt(3.0 t i + 2.0 t2 j + 5.0 )
v = 3.0 i + 2x2 t2-1 j + 0
v = 3.0 i + 4 t j
Hence option (b) is the correct answer.
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