In the graph of x versus t in fig{attached};
(a.) find the average velocity between the times t=0 & t=2sec.
(b.) Find the instantaneous velocity at t=2sec. by measuring the slope of tangent line indicated.

Question

In the graph of x versus t in fig{attached}; 
(a.) find the average velocity between the times t=0 & t=2sec. 
(b.) Find the instantaneous velocity at t=2sec. by measuring the slope of tangent line indicated.

maheshmeghwal9 · Answer

attachment

campbell_st · Answer

average velocity = change in x over change in t

                                 ( 2 - 0)/(2 -0) = 1 metre per second

the instantaneous at t = 2

find the gradient of the tangent use the points (2, 2) and (3, 4)

the instantaneous velocity at t = 2 in 2 metres per second

maheshmeghwal9 · Answer

but what if the tangent was increased then we would get different instantaneous velocity;
wouldn't we?

maheshmeghwal9 · Answer

@campbell_st

campbell_st · Answer

you do... thats why its instantaneous... 

the gradient of the tangent at a given point gives the instantaneous velocity

maheshmeghwal9 · Answer

but then there will be so many instantaneous.
& I think at t=2 sec, there must be only one inst. velocity.
what should i do?

maheshmeghwal9 · Answer

@campbell_st

campbell_st · Answer

thats correct.... differentiating the function gives the equation for the tangent... so by substituting a value into the 1st derivative you will get the instantaneous change

maheshmeghwal9 · Answer

I couldn't understand:(

maheshmeghwal9 · Answer

becoz i have learned that there is only one inst. velocity

campbell_st · Answer

ok... in calculus... you learn a process called differentiation... it givens the equation for instantaneous change.... 

there are an infinite number of instant velocities.... 

as an example... if you drove 100 kilometres in 1 hour... your average speed is 100 km/h

but in actual fact... during your journey your speed keeps changing... traffic, lights intersections.... thats what instantaneous is about

maheshmeghwal9 · Answer

but at t=2sec. there must be only one instantaneous velocity?

maheshmeghwal9 · Answer

@campbell_st Plz:)

maheshmeghwal9 · Answer

@KingGeorge Plz help:)

shubhamsrg · Answer

i dont get what your doubt is buddy..
@campbell_st has already provided a good solution

maheshmeghwal9 · Answer

my doubt is this:)
If we draw a tangent like this instead of first attachment
will not be our inst. velocity  different?

maheshmeghwal9 · Answer

@shubhamsrg

maheshmeghwal9 · Answer

u see both attachments:)

shubhamsrg · Answer

both lines are exactly the same! o.O

maheshmeghwal9 · Answer

then does it not depend on tangent?
then what does it depend on?

shubhamsrg · Answer

you are finding the slope of that line,,how does it matter how long you sketch that line,,
the slope is constant..(ofcorse)

maheshmeghwal9 · Answer

?

maheshmeghwal9 · Answer

Please say in hindi if u can:)

shubhamsrg · Answer

hmmn..
dekho..tumhe 2 sec pe inst vel nikalni hai,,wo us point pe tangent ki slope nikalne se ayegi..
tumhari given line,,ques me diya hai ki (2,2) aur (3,4) se pass hoti hai
slope ho jayega  (4-2)/(3-2) = 2
x vs t graph hai ye
slope hota hai dx/dt
aur dx/dt velocity hota hai
kya ye clearer tha?
and by the way,,even i love akshay kumar! :D

maheshmeghwal9 · Answer

thanx: D I gt it now:)

shubhamsrg · Answer

phew! :P

maheshmeghwal9 · Answer

haha:)

maheshmeghwal9 · Answer

I m so confused over these I can't tell.

maheshmeghwal9 · Answer

was*

shubhamsrg · Answer

hmmn..nevermind,,you in class XI ? studying from NCERT? CBSE? :P

maheshmeghwal9 · Answer

XII CBSE

maheshmeghwal9 · Answer

Doing IIT

shubhamsrg · Answer

doing IIT ? you mean studying for IIT ?

maheshmeghwal9 · Answer

ya:) lol

shubhamsrg · Answer

hmmn,,i cleared XII CBSE this year only,,and failed miserable in IIT and BITS :(
best of luck to you though..

shubhamsrg · Answer

miserably*

maheshmeghwal9 · Answer

sorry to hear that but u will succeed too & thanx for the comment:)

shubhamsrg · Answer

hmmn.. :|

maheshmeghwal9 · Answer

kya hua meri bat nahin samjhe kya?

maheshmeghwal9 · Answer

sorry but i have less knowledge about similey:(

shubhamsrg · Answer

bilkul samjha..lekin ab kya suceed hounga!! saal waal nahi drop kar raha main,,hopefully kisi chote mote college se maths hons, kar lunga aur MBA wagerah ke liye pursue karunga :/

maheshmeghwal9 · Answer

achcha magar ab uske liye Best of Luck:)

maheshmeghwal9 · Answer

i mean MBA:)

shubhamsrg · Answer

hmmn,,lets see..

maheshmeghwal9 · Answer

k!

maheshmeghwal9 · Answer

I have my last question now:)
Would u mind looking @ that:)

maheshmeghwal9 · Answer

?

shubhamsrg · Answer

whats this " :) "all the time ? :P
and alright,,i may have a look at that ;)

maheshmeghwal9 · Answer

ya i have made a habit of that becoz I don't know any other similey. LOL
By the way, my question is this: -
Find the instantaneous velocity @ t=0.75sec.

maheshmeghwal9 · Answer

Here is no tangent so i have problem:(

shubhamsrg · Answer

no tangent given in the ques? you'll have to assume one right ?

shubhamsrg · Answer

hmmn

maheshmeghwal9 · Answer

ya k! but how to assume

shubhamsrg · Answer

well the graph upto 0.75 secs seems to quite straight,,
so i guess thats what the ques might want you to do..

maheshmeghwal9 · Answer

?

shubhamsrg · Answer

|dw:1339667179943:dw|

maybe this helps?