A particle P moves in a straight line,starting from rest at the point O. At time t seconds after leaving O, the acceleration a ms^-2, of P is given by
a=4+12t
Calculate the distance traveled by P in the third second.

Question

A particle P moves in a straight line,starting from rest at the point O. At time t seconds after leaving O, the acceleration a ms^-2, of P is given by 
a=4+12t
Calculate the distance traveled by P in the third second.

anonymous · Answer

Thanks for having a look anyway...

anonymous · Answer

im lost D: but ill tag sum ppls c: 
@AccessDenied 
@anonymous_user 
@ememlove 
@ganeshie8

anonymous · Answer

I know the answer, if that helps... its 48m

ganeshie8 · Answer

familiar with integrals/derivatives, right ?

anonymous · Answer

yes

ganeshie8 · Answer

$  a =  4+12t$

$ \implies  v(t) - v(0) =  \int \limits_0^t  4+12t ~dt$

Since the particle started from rest, $v(0) =  0$

$ \implies  v(t) -0 =  \int \limits_0^t  4+12t ~dt$

ganeshie8 · Answer

evaluate the integral, 
what do u get ?

anonymous · Answer

$$4t+6t ^{2}$$

ganeshie8 · Answer

yup !

ganeshie8 · Answer

$ v(t)  =  4t+6t^2$

$\implies s(t) -s(0)  = \int \limits_0^t 4t+6t^2~dt$

since the particle started from Origin, $s(0) = 0$

$\implies s(t) -0  = \int \limits_0^t 4t+6t^2~dt$

ganeshie8 · Answer

evaluate the integral

anonymous · Answer

$$2t ^{2}+3t ^{3}$$

ganeshie8 · Answer

yup ! thats the displacement function :

$s(t) =    2t^2 + 3t^3$

anonymous · Answer

So what needs to be done now...

ganeshie8 · Answer

Calculate the distance traveled by P in the $third$  second.

ganeshie8 · Answer

displaccement function :  $s(t) =    2t^2 + 3t^3$

plugin $t = 3$,
distance travelled in 3rd second :
$s(3) =    ?$

anonymous · Answer

99

ganeshie8 · Answer

$\large \color{red}{\checkmark}$

anonymous · Answer

But in my book it says 48

anonymous · Answer

So is this a typo in the book, or is our answer incorrect...

ganeshie8 · Answer

it would be unwise to call the textbook has a typo, lets check our work again

ganeshie8 · Answer

btw, point O is at the center (0,0) right ?

anonymous · Answer

I would assume

anonymous · Answer

yes it is.

ganeshie8 · Answer

Found the mistake !

ganeshie8 · Answer

$\implies s(t) -0  = \int \limits_0^t 4t+6t^2~dt$

ganeshie8 · Answer

^evaluate the integral,
what do u get ?

anonymous · Answer

$$2t ^{2}+3t ^{3}$$

anonymous · Answer

+c

anonymous · Answer

maybe?

anonymous · Answer

I have no idea.....

ganeshie8 · Answer

nope

ganeshie8 · Answer

$\implies s(t) -0  = \int \limits_0^t 4t+6t^2~dt $

$\implies s(t)= 2t^2 +   2t^3$

right ?

ganeshie8 · Answer

thats our first mistake,
we made another mistake in interpreting what the question is asking us to find out

ganeshie8 · Answer

Calculate the distance traveled by P in the third second.
                                                     ^^^^^^^^^^^^^^^^^

ganeshie8 · Answer

quesiton is about finding the distance travelled between t = 2 and t = 3 only

anonymous · Answer

t=2?

ganeshie8 · Answer

so you need to find out :  $\large  s(3) - s(2)$
if that makes any sense...

anonymous · Answer

How did you derive t=2 from the question?

anonymous · Answer

wouldnt it be t=0 and t=3

ganeshie8 · Answer

t = 0 and t=  3 wud be the distance travelled "in 3 seconds"

ganeshie8 · Answer

but the question is asking u to find distance travelled "in the 3rd second"

ganeshie8 · Answer

see the difference ?

anonymous · Answer

now i get it...

ganeshie8 · Answer

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