Final answer:
The total displacement of the ball between times t=1 second and t=6 seconds is 180 ft.
Step-by-step explanation:
The total displacement of the ball between times t=1 second and t=6 seconds can be found by calculating the area under the velocity-time graph.
First, we need to find the area of the trapezoid formed by the velocity-time graph.
The formula to calculate the area of a trapezoid is A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the parallel sides and h is the height.
In this case, the parallel sides of the trapezoid are 82 ft/s and -46 ft/s, and the height is 5 seconds.
Therefore, the total displacement of the ball between times t=1 second and t=6 seconds is (82 + -46) * 5 / 2 = 180 ft.