Question 1

Refer to the diagram above. A particle moves along the x-axis from an initial position $$x_i = 12\,\mathrm{m} at$$ $$t_i = 1\,\mathrm{s} to a $$final position $$x_f = 4\,\mathrm{m} at$$ $$t_f = 3\,\mathrm{s}. $$What is the displacement of the particle during this interval?

Accepted Answer

$$\Delta x = x_f - x_i = 4\,\mathrm{m} - 12\,\mathrm{m} = -8\,\mathrm{m}$$

Question 2

Based on the diagram, what is the average velocity of the particle between $$t_i = 1\,\mathrm{s}$$ and $$t_f = 3\,\mathrm{s}$$?

Accepted Answer

$$v_{av} = \frac{\Delta x}{\Delta t} = \frac{-8\,\mathrm{m}}{2\,\mathrm{s}} = -4\,\mathrm{m/s}$$

Question 3

If the particle in the diagram continued moving with the same average velocity, what would its position be at $$t = 5\,\mathrm{s}$$?

Accepted Answer

$$x = x_f + v_{av} (t - t_f) = 4\,\mathrm{m} + (-4\,\mathrm{m/s})(5\,\mathrm{s} - 3\,\mathrm{s}) = 4\,\mathrm{m} - 8\,\mathrm{m} = -4\,\mathrm{m}$$

Question 4

What does the negative sign in the displacement $$\Delta x = -8\,\mathrm{m}$$ indicate about the particle's motion?

Accepted Answer

The particle moved in the negative x-direction (to the left on the axis).

Question 5

Suppose the particle started at $$x = 0 at$$ $$t = 0$$ and moved to $$x = 12\,\mathrm{m} at$$ $$t = 1\,\mathrm{s}$$, then to $$x = 4\,\mathrm{m} at$$ $$t = 3\,\mathrm{s}. $$What is the average velocity for the entire interval from $$t = 0 to$$ $$t = 3\,\mathrm{s}$$?

Accepted Answer

$$v_{av} = \frac{4\,\mathrm{m} - 0\,\mathrm{m}}{3\,\mathrm{s} - 0\,\mathrm{s}} = \frac{4}{3}\,\mathrm{m/s}$$

Kinematics: Translational Motion and Projectile Motion

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