Question

WILL FAN AND MEDAL

A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on, the following velocities are recorded:
Time since brakes applied (sec): 0 2 4 6
Velocity (ft/s): 100 51 18 0
Give under- and overestimates (using all of the available data) for the distance the car traveled after the brakes were applied.

Answer 1

Heyyy, integrals huh?

Answer 2

yeah XDi

Answer 3

Is this just change in x over change in y?

i know what i would do if i were trying to estimate distance at a certain point with only 3 points, but i'm confused as to what to do with this one

Answer 4

You would multiply 2, which is the time intervals, by the height, which is the velocity.

Answer 5

2 * the sum of the time intervals? and then multiply that by the sum of the velocity intervals?

Answer 6

would that be the overestimate or the underestimate?

Answer 7

Since the function is decreasing, if you start by multiplying 100 * 2, and end with 18 * 2 that would be an overestimate.

Answer 8

If you start by multiplying 51 * 2 and ending with 0 * 2, that would be an underestimate.

Answer 9

so i got 200 and 36 for the overestimate? or do i average those?

Answer 10

No, you have to add up all the rectangles.

Answer 11

For the overestimate, you would do 2(100) + 2(51) + 2(18)

Answer 12

so 338 for overestimate

Answer 13

Correct! Can you do the underestimate?

Answer 14

i don't understand why you multiplied the 2 by the velocity?

Answer 15

for underestimate would i multiply the 6 by each of the velocity values and then add them?

Answer 16

@steve816 !!

Answer 17

Because 2 is the base of the rectangle.

Answer 18

and the height is 6?

Answer 19

The height is the value of velocity.

Answer 20

^This is the riemann sum of overestimate.