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One-Dimensional Motion

One-Dimensional Motion. Physics 1. Constant Velocity. Constant Velocity. The x d - t graph for constant velocity is linear. A common equation for any line is y = mx + b. In the graph, m is velocity ( v ), b is initial position ( x i ), and y is the final position ( x f ) after a time t.

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One-Dimensional Motion

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  1. One-DimensionalMotion Physics 1

  2. Constant Velocity

  3. Constant Velocity • The xd-t graph for constant velocity is linear. A common equation for any line is y = mx + b. In the graph, m is velocity (v), b is initial position (xi), and y is the final position (xf) after a time t.

  4. Constant Velocity • By substitution, Subtracting xi to the left hand side, Since xf – xi = Dx, this results in the expression Eq. 1

  5. Constant Acceleration

  6. Constant Acceleration • The v-t graph for constant acceleration is linear. A common equation for any line is y = mx + b. In the graph, m is acceleration (a), b is initial velocity (vi), and y is the final velocity (vf) after a time t. By substitution, Eq. 2

  7. Constant Acceleration • To find the displacement (Dx), determine the area under the v-t graph. The area can be broken into a rectangle and a triangle. The rectangle’s area is bh, where b is t and h is vi. The triangle’s are is ½bh, where b is t and h is (vf – vi).

  8. Constant Acceleration • The displacement is equal to the area of the rectangle and the area of the triangle. Dx = area of █ + area of ▲

  9. Constant Acceleration • Rearranging equation 2, Substituting into the displacement equation, Rearranging, Eq. 3

  10. Base 2 Base 1 Height Constant Acceleration • To find the displacement (Dx), determine the area under the v-t graph. The area is a trapezoid. The trapezoid’s area is ½(b1+b2)h, where b1 is vi and b2 is vf, and h is t.

  11. Constant Acceleration • Using the equation for the area of a trapezoid, another equation for displacement results. Eq. 4

  12. Constant Acceleration • An equation can be obtained by squaring both sides of Equation 2. Factoring a 2a out of the last two terms,

  13. Constant Acceleration • Substituting Equation 3 for the expression in parentheses, This results in Eq. 5

  14. Eq. 1 Eq. 2 Eq. 3 Eq. 4  Eq. 5  1-D Motion Equations

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