Part A
Answer: D) 4
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The graph given to use is the velocity of the ant at time t. Look at the graph and locate the highest point, which is at (x,y) = (4,3) where the triangular portion peaks out. They want the x coordinate or the t coordinate, so x = t = 4
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Part B
Answer: D) 7
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Side Note: I'm going to assume there's a typo and it meant to say the ant's velocity rather than position. Otherwise, it would be inconsistent with what part A is saying.
To find the total distance, we find the area under the velocity curve. Any areas below the x axis are treated as positive areas because we want the total distance (instead of the displacement)
The area of the first triangle on the left is 6 square units because
A = b*h/2
A = 4*3/2
A = 12/2
A = 6
The smaller triangle is 1 square unit since
A = b*h/2
A = 2*1/2
A = 2/2
A = 1
The total area of the two triangles combined is 6+1 = 7 square units
The total distance traveled from t = 2 to t = 8 is 7
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Part C
Answer: E) 7+pi/2
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Note: Again I'm assuming that this curve is the velocity (not position) curve
This is essentially identical to part B above. The only difference is the fact that we start at t = 0 this time instead of t = 2
So the answer to part B will be added onto the area of the semicircle
Area of semicircle = (area of full circle)/2
Area of semicircle = (pi*r^2)/2
Area of semicircle = (pi*1^2)/2
Area of semicircle = pi/2
Therefore, we add on pi/2 to the previous answer (back in part B) of 7
That's why the final answer here is 7+(pi/2) or simply 7+pi/2