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
metres and t in second. What will be the position
of this particle when it achieves maximum speed
along the positive x-direction?

(1) 24 m
(2) 32 m
(3) 54 m
(4) 81 m
​

Answer 1

hi

the velocity we will get by differentiating x in terms of t we get

v = 18 t - 3 t2        the RHS is quadratic expression of form a x2 + b x + c  

will attain max value  when x = - b / 2a  

a = -3      b = 18      c = 0     put this value  we will get

t = -18 / 2 (- 3) = 3

and put this value of t in the equation  

x=9t2-t3  

we will get x = 54

Answer 2

Answer:

• we will get the value of x is 54m.