(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle is moving in the xy plane with velocity [itex]\vec{v}(t)=v_x(t)\vec{i}+v_y(t)\vec{j}[/itex] and acceleration [itex]\vec{a}(t)=a_x(t)\vec{i}+a_y(t)\vec{j}[/itex]. By taking the appropiate derivative show that the magnitude of v can be constant only if [itex]a_xv_x+a_yv_y = 0[/itex]

2. Relevant equations

3. The attempt at a solution

So I know that in order for velocity to have a constant magnitude then acceleration must = 0.

Since acceleration is the derivative of velocity and dv/dt=0 iff v=some constant.

expanding the LHS:

[tex]\frac{d\vec{v}(t)}{dt}=0[/tex]

[tex]\frac{dv_x(t)}{dt}\vec{i}+\frac{dv_y(t)}{dt}\vec{j} = 0[/tex]

[tex]a_x(t)\vec{i}+a_y(t)\vec{j} = 0[/tex]

since i,j are unit vectors and do not equal 0 the components of acceleration must = 0.

[tex]a_x(t)=a_y(t)=0[/tex]

But it's also possible for [itex]a_x=-a_y[/itex] in which case the acceleration would still = 0 so is this a proof really correct?

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# Homework Help: Prove Velocity is constant

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