The position co-ordinate of a particle that is confined to move along a straight line is given by $$\LARGE{x= 2t^3-24t+6}$$ where 'x' is measured from a convenient origin & 't' is in seconds. Determine the distance travelled by the particle during the interval from
"t=1 sec. to t =4 sec".

Question

The position co-ordinate of a particle that is confined to move along a straight line is given by $$\LARGE{x= 2t^3-24t+6}$$ where 'x' is measured from a convenient origin & 't' is in seconds. Determine the distance travelled by the particle during the interval from 
"t=1 sec. to t =4 sec".

maheshmeghwal9 · Answer

Its answer is 74meters.
But how?

maheshmeghwal9 · Answer

@mathslover @rajathsbhat Please help:)

maheshmeghwal9 · Answer

I think we r asking to solve for distance not displacement
so we can't do only put values

anonymous · Answer

any idea, @mathslover?

mathslover · Answer

no ! but i have the link of the solution can i give it ?

maheshmeghwal9 · Answer

ya of course:)

mathslover · Answer

so here i go with the link :

mathslover · Answer

is this better one ?

mathslover · Answer

@rajathsbhat wht do u think ? is that right ? acc. to me it seems to be

maheshmeghwal9 · Answer

@mathslover I think one point is to be noted that in the last part u have found displacement but we need distance
& one more think at t=2 seconds v=0
u will see it

maheshmeghwal9 · Answer

one more thing*

anonymous · Answer

*trying hard to figure out what it all means*
*haven't slept in 23 hours....* --.--

mathslover · Answer

k np @rajathsbhat u can take rest now .. @maheshmeghwal9 let me think abt this deeper :)

maheshmeghwal9 · Answer

ok:)

maheshmeghwal9 · Answer

@rajathsbhat u must sleep now:)

anonymous · Answer

thx, @mathslover. Appreciate it :)

mathslover · Answer

ur welcome

mathslover · Answer

i am just totally confused :(

maheshmeghwal9 · Answer

ya i too .

maheshmeghwal9 · Answer

so anybody here 
Please help:)

anonymous · Answer

answer is 74....@maheshmeghwal9 said it at the beginning.

anonymous · Answer

got it! here's what i did:
first differentiate the given exp to get v(t) = 6t^2 - 24
now integrate this graph twice - first from 1 to 2, then from 2 to 4. 
answer to first will come out as -10 and the second will give 64. distance is total area under the graph. so ignore the -ve sign and add the 2 values. so 10+64 = 74m

anonymous · Answer

its answer should be  74 units. The 54 units is the displacement while 74 units is the distance.

anonymous · Answer

Answer explained by @Vaidehi09 is well explained.

anonymous · Answer

yup. disp = -10+64 = 54m
while dist = 10+64 = 74m

anonymous · Answer

@ramkrishna thank u :)

maheshmeghwal9 · Answer

sorry i was offline for sometime
but i gt ur solution @Vaidehi09 
thanx a lot:)

anonymous · Answer

sure, no prob!