Question

The position x of a particle with respect to time t along x-axis is given by x = 9t² - t³ , where x is in meters and t in seconds. What will be the position of this particle when it achieves maximum speed along +x direction?

Answer 1

Here,
x = 9t² – t³
Speed of the particle will be
v = dx/dt = 18t – 3t²
Maximizing the speed
dv/dt = 18 – 6t
dv/dt = 0
18 – 6t = 0
=> t = 3 s
So the speed will be maximum at t = 3 s
So displacement at t = 3 is given by
x = 9×(3)² – (3)³
= 54 m