Question

The position x of a particle with respect to time t along x-axis is given by $x = 9t^{2} - t^{3}$where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction?

• A. 54 m
• B. 81 m
• C. 24 m
• D. 32 m

Answer 1

Answer: (A)

54 m

Answer 2

Given, a x $9t^{2} - t^{3}$

Speed,$v = \frac{dx}{dt} = \frac{d}{dt}(9t^{2} - t^{3}) = 18t - 3t^{2}$

For maximum speed, $\frac{dv}{dt} = 0$

$\therefore$0 = 18 – 6t or t = 3s.

$\therefore{X2^{3}}_{\max}$