Question

a particle moves along a straight line OX. at a time t(in seconds) the distance X(in metres) from the particle O is given by x=40+12t-t3. how long would the particle travel before coming to rest

Answer 1

To find the point at which the partical is at rest, you should concider when the velocity is zero. To do this, I would take the derivative of the equation of motion, leaving you with \[x' = 12 - 3t^2\] next you set x' (the velocity) to zero and solve for t. which will give you \[\sqrt{4}=t= \pm2\] In my mind at very least, calculus makes these kind of questions much much easier.

Answer 2

yes till here i solved but now distance travelled in that portion i m unable to solve how to do that

Answer 3

wats the problem after differentiating the equation then put it equal to zero and then find t

Answer 4

the ans of this question is 16 m given but my ans is not coming

Answer 5

thnq guys for helping.......

Answer 6

np........

Answer 7

oh, I just solved for time up above, sub the value (2) into the original equation to get the distance. \[x=40+12(2)-(2)^3= 56\] minus the 40m initial position gives you 16 m travelled.