The position x of a particle with respect to time t along X-axis is given by where x is in metres and t in second. What will he the position of this particle when it achieves maximum speed along the positive x-direction?
The position x of a particle w.r.t. time t along X-axis,
…(i)
Differentiating Eq. (i) w.r.t. time, we get speed, i.e.
…(ii)
Again, differentiating Eq. (ii) w.r.t. time, we get acceleration, i.e.
…(iii)
Now, when speed of particle is maximum, its acceleration is zero.
a = 0
t = 3 s
Putting in Eq. (i), we obtain position of particle at that time