Find the corresponding graphs for the distance-time graphs

[chwala]

then this should be easy,
$v(t)= 3t^2-6t$
$x(t)=∫vdt$
$x(t)=t^3-3t^2+k$
with condition, $x(t=0.4)=0$
we have, $x(t)=t^3-3t^2+0.416$ as the required equation.

 

[BvU]

then this should be easy,

Any particular reason you round off the 3.66 to 3 ?
And modify the condition $\ x(0) = 0\$ to $\ x(0.4) = 0\$ ?

 

[chwala]

Any particular reason you round off the 3.66 to 3 ?
And modify the condition $\ x(0) = 0\$ to $\ x(0.4) = 0\$ ?

I was working on equation $f$ and i considered its turning point to be points$(1,-3)$ ... and on checking graph$b$ i can see that when $x=0, t=0.4$. If you want me to specifically use your $v(t)$ with turning points $(1,-3.66)$then
we have $v(t)= 3.66t^2-7.32t$ integrating and applying initial condition, $x(0)=0$ yields,
$x(t)= 1.22t^3-3.66t^2$ as the required equation.

 

[BvU]

I was working on equation $f$ and i considered its turning point to be points$(1,-3)$ ... and on checking graph$b$ i can see that when $x=0, t=0.4$.
If you want me to specifically use your $v(t)$ with turning points $(1,-3.66)$then

The idea was that you would NOT look at any graphs, but simply do the integration. And indeed:

we have $v(t)= 3.66t^2-7.32t$ integrating and applying initial condition, $x(0)=0$ yields,
$x(t)= 1.22t^3-3.66t^2$ as the required equation.

Is perfect!
And, to top if off with a picture as prize: the graph looks exactly like figure (b) :

​

Now there is really nothing more to be done with this exercise, so: on to the next !
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[chwala]

Thank you Bvu, i am assuming you are a Professor...you have great insight...thank you sir. I have learned on the behaviour of functions and their derivatives (considering the fact that the equation of the function has not been given) particularly on the aspect of moving from negative to positive for eg considering a function which implies the converse i.e positive-negative when it comes to its derived function. I also learned something on inflection points implying either a maximum or a minima on corresponding given functions.

 

[BvU]

assuming you are a Professor

Haha! If only I were --- I could talk all kinds of nonsense and people would swallow it just because of the title !

Old dutch saying: flattery will get you nowhere

Now on to the next exercise !

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