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Math Help - proof involving vectors

  1. #1
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    proof involving vectors

    Show that if a particle moves with constant speed, then the
    velocity and acceleration vectors are orthogonal.
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  2. #2
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    If v(t),\quad a(t) = v'(t),\quad s(t) = \left\| {v(t)} \right\| are the velocity, acceleration, and speed functions, then recall that s'(t) = \frac{{v(t) \cdot v'(t)}}{{\left\| {v(t)} \right\| }} = \frac{{v(t) \cdot a(t)}}{{\left\| {v(t)} \right\| }}.
    But because the speed is constant, it must be the case that s'(t) = 0.
    That in turn implies that {v(t) \cdot a(t)}=0.
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