Question

What is the net distance traveled by the ant over the time interval 0 ≤ t ≤ 8?

Answer 1

So I find the area under the first semicrcle, the big triangle, and the small triangle?

Answer 2

what is that graph of, velocity or displacement?

Answer 3

velocity

Answer 4

ok then we can use geometry and calculate the areas bounded by the curve and the x axis

Answer 5

the first shape is a semicircle. we know from geometry the area of a circle

Answer 6

then take half of that area

Answer 7

A= 1/2 pi r^2 = 1/2 pi 1^2 = pi/2

Answer 8

correct

Answer 9

The area of the big triangle is 1/2 bh = 1/2 (4) (3) = 1/2 (12) = 6

Answer 10

The area of the small triangle is 1/2 bh = 1/2 (2) (1) = 1/2 (2) = 1

Answer 11

Therefore I have 6+1 +pi/2 = 7 +pi/2 right?

Answer 12

Actually I minus the 1 and get 6-1 +pi/2 = 5 +pi/2 right?

Answer 13

@perl

Answer 14

well the question says 'net distance'

Answer 15

So I minus the 1 because it is negative.

Answer 16

Under the x-axis.

Answer 17

correct, we will subtract (i think)

Answer 18

Well adding it means it would not equal any of my answers, so I'll assume we subtract. Also, the second part of the question asks for the total distance and there I would add the 1 to get 7 +pi/2.

Answer 19

According to this website
net distance is the same as displacment
http://mrkhadem.com/net_and_total_distance_traveled.htm

Answer 20

right

Answer 21

Alright thank you very much! You really helped me out and made it easy.