Michael began driving a car on a straight track due north at t=0 seconds. After 6 seconds he stopped the car and began driving in reverse, south, for another two seconds, and then he stopped again. The graph below gives the velocity of the car, in meters per second, for the 8 seconds while Michael was driving it.
https://s.yimg.com/hd/answers/i/2151e28819d6423a82881c243089ad81_A.jpeg?a=answers&mr=0&x=1399577503&s=3aa00a663f83ff80e9944dec5c0a6960
a. Make an argument as to whether or not Michael passed over his original starting location while he was driving in reverse.
b. Write an expression, in terms of v(t), that would give Michael's, change in position during the 8 seconds he was driving.
a. It looks like the area under the southbound side is greater than the northbound side so he did pass over the original starting location.
b. For v(t) I came up with a piecewise function:
for 0≤x≤6 -(1/20)x(x-6)
for 6≤x≤8 3(x-6)(x-8)
to find the change in position, you would need to integrate the function from 0 to 6 and 6 to 8 and subtract
I made a demo in Geogebra that allows you to modify the north and south velocities to see how it affects the position