Two particles at time t = 0 have left the same point. Using the velocity-time graphs, determine the coordinates and time of the new meeting of the particles.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

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    <h3> Statement </h3>
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        $1.2.2.$ Two particles at time $t = 0$ have left the same point. Using the velocity-time graphs, determine the coordinates and time of the new meeting of the particles.

    <h3>Solution</h3>
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1. Equations of motion of particles.

$${x_{1}(t) = v_{1}t, \quad x_{2}(t) = \frac{at^2}{2}}$$

2. The velocity of the first particle and acceleration of the second particle are determined by the given dependence $v = f(t)$:

$${v_{1} = 2\\; \frac{m}{s}}, \quad a \equiv 0.33\\; \frac{m}{s^{2}}.$$

3. Particle encounter condition:

$$x_{1}(t_{z}) = x_{2}(t_{z}). \quad t_{z} = \frac{2v_{z}}{a} = 12\\; c, \quad x_{z} = 24\\; m.$$

    <h4>Answer</h4>
    <p>
        From the region bounded by the angle $α = 2 \\, \arcsin \frac{u}{v}$ with vertex at the point $A$, bisected by a freeway.
    </p>


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