- #1
PFuser1232
- 479
- 20
Homework Statement
Consider two points located at ##\vec{r}_1## and ##\vec{r}_2## separated by a distance ##r##. Find a time-dependent vector ##\vec{A}(t)## from the origin that is at ##\vec{r}_1## at time ##t_1## and at ##\vec{r}_2## at time ##t_2 = t_1 + T##. Assume that ##\vec{A}(t)## moves uniformly along the straight line between the two points.
Homework Equations
$$\vec{A}(t) = \vec{A}(t_1) + \int_{t_1}^t \frac{d\vec{A}}{dt'} dt'$$
$$\vec{A}(t) = \vec{A}(t_2) + \int_{t_2}^t \frac{d\vec{A}}{dt'} dt'$$
The Attempt at a Solution
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Since the time derivative of ##\vec{A}## is constant, I have pulled it out of the integral, eliminated it from both equations, and solved for ##\vec{A}(t)##. I ended up with an expression that looks too messy, though, so I don't know whether my approach (eliminating the derivative from both equations) is correct.