Question

CALCULUS QUESTION!!

Answer 1

what is it

Answer 2

i need someone to explain it step by step

Answer 3

@ganeshie8 help!!!

Answer 4

Can you find the equation for the acceleration in your graph?

Answer 5

the equation in your graph is a line
it is a line of the form y=mx+b

Answer 6

b is the y-intercept
m is the slope

Answer 7

can you see what number on the y-axis is being hit by the line?

Answer 8

so the slope is -1

Answer 9

and the y intercept would be 10?

Answer 10

yes so the acceleration function is
a(t)=-t+10

Answer 11

you can find the velocity function by integrating a(t)

Answer 12

\[v(t)=\int\limits a(t) dt=\int\limits (-t+10) dt=?\]

Answer 13

-t^2/2

Answer 14

ok and the anti-derivative of 10 is ?

Answer 15

10x+C

Answer 16

\[v(t)=\int\limits(-t+10) dt=\frac{-t^2}{2}+10t+C \\ v(t)=\frac{-t^2}{2}+10t+C \\ \]

Answer 17

now use the condition given to find C

Answer 18

then when you have that
do the following to get total distance:
\[\int\limits_{0}^{30}|v(t)| dt \]

Answer 19

oops sorry im stuck on trying to find C haha

Answer 20

do you know what this means:
"At t=0, velocity of the car is 0"

Answer 21

1/2(t-20)t =C

Answer 22

is that C?

Answer 23

no you need to apply the condition I just mentioned

Answer 24

you are given at t=0 we have v=0

Answer 25

apply that to find C

Answer 26

\[v(t)=\int\limits\limits(-t+10) dt=\frac{-t^2}{2}+10t+C \\ v(t)=\frac{-t^2}{2}+10t+C \\ \\ 0=\frac{-0^2}{2}+10(0)+C\]
that sentence told me v(0)=0
so I entered in for t, 0 and for v, 0
now can you solve for C?

Answer 27

C=0

Answer 28

yep now for finding total distance apply this formula:
\[\int\limits_{0}^{30}|v(t)| dt\]

Answer 29

oh gosh hahaha

Answer 30

and remember to use that
|v(t)|=v(t) if v(t)>0
|v(t)|=-v(t) if v(t)<0

Answer 31

wait is just solve that?

Answer 32

ill take that as a yes hahaha

Answer 33

so what number did you split your integral at?

Answer 34

i dont know.. i havnt done anything cause im confused

Answer 35

i get everything up to this step

Answer 36

Which step? determining when v is negative or positive on the interval from t=0 to t=30?

Answer 37

v=-t^2/2+10t is a parabola that is concave down
you can find when it is 0 by solve -t^2/2+10t=0
Your parabola on [0,30] will look something like this: