where x is expressed in metre and t in second. what is the work done by the force in the first two seconds? given answer is 75 J but i think that the answer is wrong.
F = ma
= 0.5Xa
now, x = 3t2+4t+5
=> a = 6
therefore, F = 3N
Now, WD = int(F.dx) = int(3.dx)
Also, dx = (6t+4)dt
therefore, WD = int(3 x (6t+4)dt
= 3[3t2+4t] from 0 to 2
= 3[3(4)+4(2)]
= 3(12+8)
= 60 J
Ya, i think given answer is wrong. Did u also got this answer???
= 0.5Xa
now, x = 3t2+4t+5
=> a = 6
therefore, F = 3N
Now, WD = int(F.dx) = int(3.dx)
Also, dx = (6t+4)dt
therefore, WD = int(3 x (6t+4)dt
= 3[3t2+4t] from 0 to 2
= 3[3(4)+4(2)]
= 3(12+8)
= 60 J
Ya, i think given answer is wrong. Did u also got this answer???
yes i got the same answer too!!
Hello,
to ankul: int(Fdx) is to be used when the force is variable, here it is not the case. x=3t2+4t+5,
differentiating twice you get accl.=6,
therefore f=ma, so f=.5*6=3N.
W=F X (x)
x in 2 seconds is found out by putting t=2 in x=3t2+4t+5, you get x=25m.
therefore w=3 X 25=75 J.
tell me if it is correct.
to Jeffrey John:
U r right but check that u wrote x in 2 sec = 3(4)+4(2)+5 which actually gives position of the particle at t = 2. Initially at t=0, x = 5. Therefore, displacement = 25-5 = 20.
therefore, WD = 20 X 3 = 60J.
I think there's something wrong with language of ques.
It should have been that position of particle is given by x = 3t2+4t+5 otherwise it makes no sense to give distance travelled by this expression as one can't say that dist. travelled at t = t1 is this much.
U r right but check that u wrote x in 2 sec = 3(4)+4(2)+5 which actually gives position of the particle at t = 2. Initially at t=0, x = 5. Therefore, displacement = 25-5 = 20.
therefore, WD = 20 X 3 = 60J.
I think there's something wrong with language of ques.
It should have been that position of particle is given by x = 3t2+4t+5 otherwise it makes no sense to give distance travelled by this expression as one can't say that dist. travelled at t = t1 is this much.
the answer is defenitely 60J and ankul is going right.
;-)
;-)
(Edited by INDIANET @IIT-JEE - Monday, 19 June 2006, 06:15 PM)