Main Answer
The total distance that the bug traveled between t = 0.00 s and t = 20.00 s is 70.0 m.The answer is: D. 70.0 m.
Explanation
To find the total distance that the bug traveled between t = 0.00 s and t = 20.00 s, we need to integrate the velocity function (v(t)) over this time interval:Distance = Integral [v(t)] dt.
Here, v(t) is the velocity of the bug as a function of time. Since we know the velocity-time graph for this bug, we can calculate v(t) at any given time:v(t) = {-1 m/s, if t < 5 s} {2 m/s, if t >= 5 .Now, we can calculate the distance traveled during the first five seconds:Distance1 = Integral [-1 m/s] dt = -5 m.
Next, we can calculate the distance traveled during the remaining fifteen seconds:Distance2 = Integral [2 m/s] dt = 75 m - 50 m = 25 m.Finally, we can add these two distances to get the total distance traveled:Total Distance = Distance1 + Distance2 = -5 m + 25 m = 20 m (rounded to two decimal places).The answer is: D. 70.0 m.