Question

I gave up on this physics problem, help me please.
I will upload the picture, it's a graph!

-- what is the formula to use for such problem?

Answer 1

are you familiar with calculus?

Answer 2

if so, then you need to find the area under the velocity curve to get the total displacement

Answer 3

usually that involves an integral, but luckily, you have straight lines. That means you can break this figure up into trapezoids, rectangles and triangles

Answer 4

also, be careful about how they set up the y axis

Answer 5

no, not really, I took precal . can you give me formulas to use. thanks a lot for helping

Answer 6

first I would draw in the x axis to help you see where it's at better (see attached)

I drew the x axis in green

Answer 7

the goal is to find the area of these three regions I colored in (see attached)

Answer 8

take note that the two roots of that velocity function are at (15,0) and (70,0)

Answer 9

the areas above the curve (the blue and pink region) represent positive displacement. They move the object in the positive direction

the yellow area under the curve represents negative displacement. The object will move in the negative direction

Answer 10

finish please, I need to know this, I have many problems like this that I need to do

Answer 11

do you know how to find the area of a triangle?

Answer 12

that blue triangle has a base of 15, height of 20

Answer 13

1/2b*h

Answer 14

yes

Answer 15

what is the area of the blue triangle

Answer 16

150

Answer 17

good

Answer 18

how about the area of that yellow trapezoid?

Answer 19

how did you know that base of blue triangle is 15, it's not clear

Answer 20

do you see how the x-intercept is (15,0) ?

Answer 21

yes

Answer 22

it's not an exact number though right?

Answer 23

so the base extends from (0,0) to (15,0) making it 15 units long

Answer 24

it is

Answer 25

it's the midpoint of 10 and 20

or of 0 and 30

Answer 26

alternatively, you can find the equation of the line through (0,20) and (30,-20)

then find the x-intercept of that equation

Answer 27

so the yellow triangle goes from 15-70

Answer 28

or just find the midpoint of the segment through (0,20) and (30,-20)

that midpoint is (15,0)

Answer 29

that's base= 55

Answer 30

correct

Answer 31

yellow trapezoid, not triangle

Answer 32

but you have the right idea in mind

Answer 33

oh, yeah. thnx so i'll figure the area of all shapes, than what?

Answer 34

you add up the areas above the x axis

then subtract off the areas below the x axis

Answer 35

this will give the total displacement

Answer 36

what that be the final answer?

Answer 37

if we label the three areas A1, A2, A3 (see attached), then we can get the total displacement D to be

D = A1 - A2 + A3

notice how I'm subtracting off A2 since that area is below the x axis

Answer 38

you then add that displacement to the starting position to get the ending position

Answer 39

ending position = (starting position) + (total displacement)

Answer 40

A1= 150
A2= 750
A3= 50

150-750+50 = -550

Answer 41

very good, you nailed that part

Answer 42

the total displacement is -550, which means that this object moves 550 units in the negative direction

Answer 43

THANK YOU!! for helping :)

Answer 44

so where is the final position?

Answer 45

isn't -550?

Answer 46

it starts at _____ and moves 550 units in the negative direction ending up at _____

Answer 47

that -550 is not the answer

Answer 48

it just tells us how that position has changed

not the final position

Answer 49

starts at -10

Answer 50

right

Answer 51

yes

Answer 52

you add on (-550) to get the ending position

Answer 53

-560

Answer 54

yes

Answer 55

so it's starting position+ the total displacement = ending position

Answer 56

correct

Answer 57

cool, thank you :)

Answer 58

np