Consider the following diagram depicting the motion of a ball bouncing between two walls:

What is the total distance travelled by the ball?

Solution

From the position graph, we can track the object's position at each transition point:

At $t = 0\text{ s}$: $x_0 = 5\text{ m}$

At $t = 2\text{ s}$: $x_1 = x_0 + v_1 \cdot \Delta t_1 = 5 + 3 \cdot 2 = 11\text{ m}$

At $t = 5\text{ s}$: $x_2 = x_1 + v_2 \cdot \Delta t_2 = 11 + (-4) \cdot 3 = -1\text{ m}$

At $t = 7\text{ s}$: $x_3 = x_2 + v_3 \cdot \Delta t_3 = -1 + 2 \cdot 2 = 3\text{ m}$

Displacement: Displacement is the change in position from start to finish:

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