consta1d - Constant acceleration in one dimension A very...

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Constant acceleration in one dimension A very important special case of motion of a particle is the motion of a particle with constant acceleration along the x-axis. If the acceleration is constant then the slope of the tangent line to the v x versus t curve is constant. This can only pertain to a linear v x versus t graph, [c.f, y(x) = mx + b]. Using the definition of a x = dv x /dt , multiplying this by dt and integrating gives, v x (t) = v ox + a x t (1d, a x =constant). In this equation, v ox is the velocity of the particle when the stopwatch reads zero, "a x " is the constant acceleration of the particle, "t" is the time, and v x (t) is the velocity at time t. As will be shown in class using calculus, x(t) - x o , is the area under the v x (t) versus t curve between time zero and time, t. Therefore, using v x = dx/dt, multiplying by dt and then integrating gives, x(t) = x o + v ox t + 1/2 a x t 2 (1d, a=constant). (Note: memorize this only, since dx/dt gives the v x (t) eq. .)
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In the equation, x o is the position of the particle when the stopwatch reads zero, and x(t) is the position at time "t".
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