Question

Suppose that a car is moving along a straight road, and the distant traveled *t* hours after starting from rest is given by f(t) = 2t^2 + 60t. Find the average velocity of the car over the time intervals [0,2] and [1,2]. Find the instantaneous velocity at t = 1 and t = 2

Answer 1

Well, first differentiate the equation given to find the velocity function

Answer 2

Yes, i have the velocity function f’(x) = 4t+60. What do i do next?

Answer 3

I won’t drag this question for too long. Just guide me what to do :)

Answer 4

By definition, the average velocity in the interval [a,b] is

\[\bar v= \frac{ f(b)-f(a) }{ b-a }\]

Whereas the instantaneous velocity (velocity at an instant c) is

\[v(c)= \lim _{h \rightarrow0}\frac{ f(c+h) -f(c)}{ h }\]

Answer 5

I have found the instantaneous velocity at t = 1 and t = 2. Wait let me draw. One second

Answer 6

Sorry my pencil died..plz give me 1 minute to charge it. Really appreciated ur patience 😀

Answer 7

Those r the instantaneous velocities at t =1 and t=2.

Answer 8

The answers are correct, apply the formula to find the average velocities

Answer 9

Now how do I find the avg velocity of the car between interval [0,2] and [1,2]?

Answer 10

I have written the definition

Answer 11

Yes

Answer 12

What do i plugin in that equation?

Answer 13

a and b are the time in the interval

Answer 14

Plz wait let me draw

Answer 15

Idk what to plugin into the equation

Answer 16

Because if I do this...

Answer 17

Is this it?

Answer 18

\[f(b )\neq b\]

Answer 19

\[f(2)\neq2\]

Answer 20

Can u help me label the points plz

Answer 21

What is f(t)?

Answer 22

Is it a time function?

Answer 23

yes

Answer 24

[a,b] is an interval like going from t=a to t=b

Answer 25

Similar to y2 - y1/ X2-x1?

Answer 26

f(2)= ???

f(0)= ??????

Answer 27

Do I have to solve the function for those values? Ok let me draw

Answer 28

yes

Answer 29

Yes, good so far, continue

Answer 30

Do I have to do that with the other point now?

Answer 31

Calculate the average velocity in the interval [0,2]?

Answer 32

The question is ...find the avg velocity of the car over the intervals [0,2] and [1,2]

Answer 33

Yes, there are 2 questions

Answer 34

So far we have calculated f(0) and f(2)

Answer 35

So what do I do with f(2)=128 and f(0)=0?

Answer 36

\[\bar v= \frac{ f(2)-f(0) }{ 2-0 }\]

Answer 37

Omg wait

Answer 38

Is this it?

Answer 39

Yes, that's correct, do the the calculation in the interval [1,2] ?

Answer 40

Omg... ok wait plz

Answer 41

Is this it?

Answer 42

Plz check my work

Answer 43

Nope, the answer is 64 and 66... I’m getting 33 and 64

Answer 44

The avg velocity should be very close to the instantaneous velocity...

Answer 45

The first answer for [0,2 ] is correct, check the calculation for [1,2]?

Answer 46

Where could I go wrong?

Answer 47

The interval is [2,1] and you are subtracting 2-0

Answer 48

Oh my gook....good catch mate...lol

Answer 49

Oh nvm ur good. We have finished the question..

Answer 50

Thanks a lot narad. Your the best dude..

Answer 51

You are welcome

Answer 52

I was using the leibniz’s principal to solve the equation... it took me like an hour to substitute and solve the limit... by the time i got the answer... it turned out it was just the first derivative of the equation...which is just 4t + 60......i was so infuriated....because i knew the method looked similar to the leibniz’s principal... which is f(b)-f(a)/b-a..... but i never figured it out myself.. soo i had to come here for the help...

Answer 53

\(\color{#0cbb34}{\text{Originally Posted by}}\) @MLYS2
your a girl
\(\color{#0cbb34}{\text{End of Quote}}\)
What makes you think so? He's not a girl..